blob: 5029675112322593ccd23ce7dd22453e37febae7 (plain)

ofs	hex dump	ascii
0000	cb 0d 0d 0a 00 00 00 00 85 fa a7 68 27 a9 00 00 e3 00 00 00 00 00 00 00 00 00 00 00 00 05 00 00	...........h'...................
0020	00 00 00 00 00 f3 4c 02 00 00 97 00 64 00 5a 00 64 01 64 02 6c 01 6d 02 5a 02 01 00 64 01 64 03	......L.....d.Z.d.d.l.m.Z...d.d.
0040	6c 03 6d 04 5a 04 6d 05 5a 05 01 00 64 01 64 04 6c 06 6d 07 5a 07 01 00 64 01 64 05 6c 08 5a 09	l.m.Z.m.Z...d.d.l.m.Z...d.d.l.Z.
0060	64 01 64 06 6c 0a 6d 0b 5a 0b 6d 0c 5a 0c 01 00 67 00 64 07 a2 01 5a 0d 02 00 65 0b 64 08 ab 01	d.d.l.m.Z.m.Z...g.d...Z...e.d...
0080	00 00 00 00 00 00 02 00 65 0b 64 09 ab 01 00 00 00 00 00 00 65 09 6a 1c 00 00 00 00 00 00 00 00	........e.d.........e.j.........
00a0	00 00 00 00 00 00 00 00 00 00 64 1f 64 0a 84 01 ab 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00	..........d.d...................
00c0	ab 00 00 00 00 00 00 00 5a 0f 65 09 6a 1c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	........Z.e.j...................
00e0	64 1f 64 0b 84 01 ab 00 00 00 00 00 00 00 5a 10 64 0c 84 00 5a 11 64 0d 84 00 5a 12 02 00 47 00	d.d...........Z.d...Z.d...Z...G.
0100	64 0e 84 00 64 0f 65 13 ab 03 00 00 00 00 00 00 5a 14 64 10 84 00 5a 15 64 11 84 00 5a 16 65 09	d...d.e.........Z.d...Z.d...Z.e.
0120	6a 1c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 1f 64 12 84 01 ab 00 00 00 00 00	j...................d.d.........
0140	00 00 5a 17 64 13 84 00 5a 18 02 00 65 0b 64 14 ab 01 00 00 00 00 00 00 02 00 65 09 6a 1c 00 00	..Z.d...Z...e.d...........e.j...
0160	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 15 ac 16 ab 01 00 00 00 00 00 00 64 17 84 00	................d...........d...
0180	ab 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 5a 19 65 09 6a 1c 00 00 00 00 00 00 00 00 00 00	................Z.e.j...........
01a0	00 00 00 00 00 00 00 00 64 20 64 18 84 01 ab 00 00 00 00 00 00 00 5a 1a 02 00 65 0b 64 08 ab 01	........d.d...........Z...e.d...
01c0	00 00 00 00 00 00 02 00 65 0b 64 09 ab 01 00 00 00 00 00 00 02 00 65 09 6a 1c 00 00 00 00 00 00	........e.d...........e.j.......
01e0	00 00 00 00 00 00 00 00 00 00 00 00 64 19 ac 1a ab 01 00 00 00 00 00 00 64 1f 64 1b 84 01 ab 00	............d...........d.d.....
0200	00 00 00 00 00 00 ab 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 5a 1b 64 1c 84 00 5a 1c 64 1d	......................Z.d...Z.d.
0220	84 00 5a 1d 02 00 65 0b 64 08 ab 01 00 00 00 00 00 00 02 00 65 0b 64 09 ab 01 00 00 00 00 00 00	..Z...e.d...........e.d.........
0240	65 09 6a 1c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 1e 84 00 ab 00 00 00 00 00	e.j...................d.........
0260	00 00 ab 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 5a 1e 79 05 29 21 7a 4c 0a 3d 3d 3d 3d 3d	..................Z.y.)!zL.=====
0280	3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 0a 43 79 63 6c 65 20 66 69 6e 64 69 6e	===================.Cycle.findin
02a0	67 20 61 6c 67 6f 72 69 74 68 6d 73 0a 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d	g.algorithms.===================
02c0	3d 3d 3d 3d 3d 0a e9 00 00 00 00 29 01 da 0b 64 65 66 61 75 6c 74 64 69 63 74 29 02 da 0c 63 6f	=====......)...defaultdict)...co
02e0	6d 62 69 6e 61 74 69 6f 6e 73 da 07 70 72 6f 64 75 63 74 29 01 da 03 69 6e 66 4e 29 02 da 13 6e	mbinations..product)...infN)...n
0300	6f 74 5f 69 6d 70 6c 65 6d 65 6e 74 65 64 5f 66 6f 72 da 08 70 61 69 72 77 69 73 65 29 07 da 0b	ot_implemented_for..pairwise)...
0320	63 79 63 6c 65 5f 62 61 73 69 73 da 0d 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 da 17 72 65 63 75	cycle_basis..simple_cycles..recu
0340	72 73 69 76 65 5f 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 da 0a 66 69 6e 64 5f 63 79 63 6c 65 da	rsive_simple_cycles..find_cycle.
0360	13 6d 69 6e 69 6d 75 6d 5f 63 79 63 6c 65 5f 62 61 73 69 73 da 10 63 68 6f 72 64 6c 65 73 73 5f	.minimum_cycle_basis..chordless_
0380	63 79 63 6c 65 73 da 05 67 69 72 74 68 da 08 64 69 72 65 63 74 65 64 da 0a 6d 75 6c 74 69 67 72	cycles..girth..directed..multigr
03a0	61 70 68 63 02 00 00 00 00 00 00 00 00 00 00 00 05 00 00 00 03 00 00 00 f3 52 02 00 00 97 00 74	aphc.....................R.....t
03c0	00 00 00 00 00 00 00 00 00 6a 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 ab	.........j...................|..
03e0	01 00 00 00 00 00 00 7d 02 67 00 7d 03 7c 02 90 01 72 0c 7c 01 80 13 7c 02 6a 05 00 00 00 00 00	.......}.g.}.|...r.|...|.j......
0400	00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 64 02 19 00 00 00 7d 01 7c 01 67	.....................d.....}.|.g
0420	01 7d 04 7c 01 7c 01 69 01 7d 05 7c 01 74 07 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 69	.}.|.|.i.}.|.t.................i
0440	01 7d 06 7c 04 72 c3 7c 04 6a 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00	.}.|.r.|.j......................
0460	00 00 00 00 00 7d 07 7c 06 7c 07 19 00 00 00 7d 08 7c 00 7c 07 19 00 00 00 44 00 5d a3 00 00 7d	.....}.|.|.....}.|.|.....D.]...}
0480	09 7c 09 7c 06 76 01 72 1d 7c 07 7c 05 7c 09 3c 00 00 00 7c 04 6a 0b 00 00 00 00 00 00 00 00 00	.|.|.v.r.|.|.|.<...|.j..........
04a0	00 00 00 00 00 00 00 00 00 7c 09 ab 01 00 00 00 00 00 00 01 00 7c 07 68 01 7c 06 7c 09 3c 00 00	.........|...........|.h.|.|.<..
04c0	00 8c 24 7c 09 7c 07 6b 28 00 00 72 13 7c 03 6a 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	..$|.|.k(..r.|.j................
04e0	00 00 00 7c 07 67 01 ab 01 00 00 00 00 00 00 01 00 8c 3c 7c 09 7c 08 76 01 73 01 8c 41 7c 06 7c	...|.g............<|.|.v.s..A|.|
0500	09 19 00 00 00 7d 0a 7c 09 7c 07 67 02 7d 0b 7c 05 7c 07 19 00 00 00 7d 0c 7c 0c 7c 0a 76 01 72	.....}.|.|.g.}.|.|.....}.|.|.v.r
0520	1b 7c 0b 6a 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0c ab 01 00 00 00 00 00	.|.j...................|........
0540	00 01 00 7c 05 7c 0c 19 00 00 00 7d 0c 7c 0c 7c 0a 76 01 72 01 8c 1b 7c 0b 6a 0b 00 00 00 00 00	...|.|.....}.|.|.v.r...|.j......
0560	00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0c ab 01 00 00 00 00 00 00 01 00 7c 03 6a 0b 00 00 00	.............|...........|.j....
0580	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0b ab 01 00 00 00 00 00 00 01 00 7c 06 7c 09 19	...............|...........|.|..
05a0	00 00 00 6a 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 07 ab 01 00 00 00 00 00	...j...................|........
05c0	00 01 00 8c a5 04 00 7c 04 72 01 8c c3 7c 05 44 00 5d 14 00 00 7d 0d 7c 02 6a 09 00 00 00 00 00	.......|.r...|.D.]...}.|.j......
05e0	00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0d 64 01 ab 02 00 00 00 00 00 00 01 00 8c 16 04 00 64	.............|.d...............d
0600	01 7d 01 7c 02 72 02 90 01 8c 0c 7c 03 53 00 29 03 61 76 04 00 00 52 65 74 75 72 6e 73 20 61 20	.}.|.r.....|.S.).av...Returns.a.
0620	6c 69 73 74 20 6f 66 20 63 79 63 6c 65 73 20 77 68 69 63 68 20 66 6f 72 6d 20 61 20 62 61 73 69	list.of.cycles.which.form.a.basi
0640	73 20 66 6f 72 20 63 79 63 6c 65 73 20 6f 66 20 47 2e 0a 0a 20 20 20 20 41 20 62 61 73 69 73 20	s.for.cycles.of.G.......A.basis.
0660	66 6f 72 20 63 79 63 6c 65 73 20 6f 66 20 61 20 6e 65 74 77 6f 72 6b 20 69 73 20 61 20 6d 69 6e	for.cycles.of.a.network.is.a.min
0680	69 6d 61 6c 20 63 6f 6c 6c 65 63 74 69 6f 6e 20 6f 66 0a 20 20 20 20 63 79 63 6c 65 73 20 73 75	imal.collection.of.....cycles.su
06a0	63 68 20 74 68 61 74 20 61 6e 79 20 63 79 63 6c 65 20 69 6e 20 74 68 65 20 6e 65 74 77 6f 72 6b	ch.that.any.cycle.in.the.network
06c0	20 63 61 6e 20 62 65 20 77 72 69 74 74 65 6e 0a 20 20 20 20 61 73 20 61 20 73 75 6d 20 6f 66 20	.can.be.written.....as.a.sum.of.
06e0	63 79 63 6c 65 73 20 69 6e 20 74 68 65 20 62 61 73 69 73 2e 20 20 48 65 72 65 20 73 75 6d 6d 61	cycles.in.the.basis...Here.summa
0700	74 69 6f 6e 20 6f 66 20 63 79 63 6c 65 73 0a 20 20 20 20 69 73 20 64 65 66 69 6e 65 64 20 61 73	tion.of.cycles.....is.defined.as
0720	20 22 65 78 63 6c 75 73 69 76 65 20 6f 72 22 20 6f 66 20 74 68 65 20 65 64 67 65 73 2e 20 43 79	."exclusive.or".of.the.edges..Cy
0740	63 6c 65 20 62 61 73 65 73 20 61 72 65 0a 20 20 20 20 75 73 65 66 75 6c 2c 20 65 2e 67 2e 20 77	cle.bases.are.....useful,.e.g..w
0760	68 65 6e 20 64 65 72 69 76 69 6e 67 20 65 71 75 61 74 69 6f 6e 73 20 66 6f 72 20 65 6c 65 63 74	hen.deriving.equations.for.elect
0780	72 69 63 20 63 69 72 63 75 69 74 73 0a 20 20 20 20 75 73 69 6e 67 20 4b 69 72 63 68 68 6f 66 66	ric.circuits.....using.Kirchhoff
07a0	27 73 20 4c 61 77 73 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d	's.Laws.......Parameters.....---
07c0	2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 20 3a 20 4e 65 74 77 6f 72 6b 58 20 47 72 61 70 68 0a 20	-------.....G.:.NetworkX.Graph..
07e0	20 20 20 72 6f 6f 74 20 3a 20 6e 6f 64 65 2c 20 6f 70 74 69 6f 6e 61 6c 0a 20 20 20 20 20 20 20	...root.:.node,.optional........
0800	53 70 65 63 69 66 79 20 73 74 61 72 74 69 6e 67 20 6e 6f 64 65 20 66 6f 72 20 62 61 73 69 73 2e	Specify.starting.node.for.basis.
0820	0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 41 20	......Returns.....-------.....A.
0840	6c 69 73 74 20 6f 66 20 63 79 63 6c 65 20 6c 69 73 74 73 2e 20 20 45 61 63 68 20 63 79 63 6c 65	list.of.cycle.lists...Each.cycle
0860	20 6c 69 73 74 20 69 73 20 61 20 6c 69 73 74 20 6f 66 20 6e 6f 64 65 73 0a 20 20 20 20 77 68 69	.list.is.a.list.of.nodes.....whi
0880	63 68 20 66 6f 72 6d 73 20 61 20 63 79 63 6c 65 20 28 6c 6f 6f 70 29 20 69 6e 20 47 2e 0a 0a 20	ch.forms.a.cycle.(loop).in.G....
08a0	20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e	...Examples.....--------.....>>>
08c0	20 47 20 3d 20 6e 78 2e 47 72 61 70 68 28 29 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 61 64 64 5f 63	.G.=.nx.Graph().....>>>.nx.add_c
08e0	79 63 6c 65 28 47 2c 20 5b 30 2c 20 31 2c 20 32 2c 20 33 5d 29 0a 20 20 20 20 3e 3e 3e 20 6e 78	ycle(G,.[0,.1,.2,.3]).....>>>.nx
0900	2e 61 64 64 5f 63 79 63 6c 65 28 47 2c 20 5b 30 2c 20 33 2c 20 34 2c 20 35 5d 29 0a 20 20 20 20	.add_cycle(G,.[0,.3,.4,.5]).....
0920	3e 3e 3e 20 6e 78 2e 63 79 63 6c 65 5f 62 61 73 69 73 28 47 2c 20 30 29 0a 20 20 20 20 5b 5b 33	>>>.nx.cycle_basis(G,.0).....[[3
0940	2c 20 34 2c 20 35 2c 20 30 5d 2c 20 5b 31 2c 20 32 2c 20 33 2c 20 30 5d 5d 0a 0a 20 20 20 20 4e	,.4,.5,.0],.[1,.2,.3,.0]]......N
0960	6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 54 68 69 73 20 69 73 20 61 64 61 70 74	otes.....-----.....This.is.adapt
0980	65 64 20 66 72 6f 6d 20 61 6c 67 6f 72 69 74 68 6d 20 43 41 43 4d 20 34 39 31 20 5b 31 5d 5f 2e	ed.from.algorithm.CACM.491.[1]_.
09a0	0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a	......References.....----------.
09c0	20 20 20 20 2e 2e 20 5b 31 5d 20 50 61 74 6f 6e 2c 20 4b 2e 20 41 6e 20 61 6c 67 6f 72 69 74 68	.......[1].Paton,.K..An.algorith
09e0	6d 20 66 6f 72 20 66 69 6e 64 69 6e 67 20 61 20 66 75 6e 64 61 6d 65 6e 74 61 6c 20 73 65 74 20	m.for.finding.a.fundamental.set.
0a00	6f 66 0a 20 20 20 20 20 20 20 63 79 63 6c 65 73 20 6f 66 20 61 20 67 72 61 70 68 2e 20 43 6f 6d	of........cycles.of.a.graph..Com
0a20	6d 2e 20 41 43 4d 20 31 32 2c 20 39 20 28 53 65 70 74 20 31 39 36 39 29 2c 20 35 31 34 2d 35 31	m..ACM.12,.9.(Sept.1969),.514-51
0a40	38 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20	8.......See.Also.....--------...
0a60	20 20 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 0a 20 20 20 20 6d 69 6e 69 6d 75 6d 5f 63 79 63 6c	..simple_cycles.....minimum_cycl
0a80	65 5f 62 61 73 69 73 0a 20 20 20 20 4e 72 02 00 00 00 29 07 da 04 64 69 63 74 da 08 66 72 6f 6d	e_basis.....Nr....)...dict..from
0aa0	6b 65 79 73 da 07 70 6f 70 69 74 65 6d da 03 73 65 74 da 03 70 6f 70 da 06 61 70 70 65 6e 64 da	keys..popitem..set..pop..append.
0ac0	03 61 64 64 29 0e da 01 47 da 04 72 6f 6f 74 da 06 67 6e 6f 64 65 73 da 06 63 79 63 6c 65 73 da	.add)...G..root..gnodes..cycles.
0ae0	05 73 74 61 63 6b da 04 70 72 65 64 da 04 75 73 65 64 da 01 7a da 05 7a 75 73 65 64 da 03 6e 62	.stack..pred..used..z..zused..nb
0b00	72 da 02 70 6e da 05 63 79 63 6c 65 da 01 70 da 04 6e 6f 64 65 73 0e 00 00 00 20 20 20 20 20 20	r..pn..cycle..p..nodes..........
0b20	20 20 20 20 20 20 20 20 fa 61 2f 68 6f 6d 65 2f 62 6c 61 63 6b 68 61 6f 2f 75 69 75 63 2d 63 6f	.........a/home/blackhao/uiuc-co
0b40	75 72 73 65 2d 67 72 61 70 68 2f 2e 76 65 6e 76 2f 6c 69 62 2f 70 79 74 68 6f 6e 33 2e 31 32 2f	urse-graph/.venv/lib/python3.12/
0b60	73 69 74 65 2d 70 61 63 6b 61 67 65 73 2f 6e 65 74 77 6f 72 6b 78 2f 61 6c 67 6f 72 69 74 68 6d	site-packages/networkx/algorithm
0b80	73 2f 63 79 63 6c 65 73 2e 70 79 72 09 00 00 00 72 09 00 00 00 19 00 00 00 73 57 01 00 00 80 00	s/cycles.pyr....r........sW.....
0ba0	f4 5c 01 00 0e 12 8f 5d 89 5d 98 31 d3 0d 1d 80 46 d8 0d 0f 80 46 da 0a 10 d8 0b 0f 88 3c d8 13	.\.....].].1....F....F.......<..
0bc0	19 97 3e 91 3e d3 13 23 a0 41 d1 13 26 88 44 d8 11 15 90 06 88 05 d8 10 14 90 64 88 7c 88 04 d8	..>.>..#.A..&.D...........d.|...
0be0	10 14 94 63 93 65 88 7d 88 04 d9 0e 13 d8 10 15 97 09 91 09 93 0b 88 41 d8 14 18 98 11 91 47 88	...c.e.}...............A......G.
0c00	45 d8 17 18 98 11 91 74 f2 00 10 0d 25 90 03 d8 13 16 98 64 91 3f d8 20 21 90 44 98 13 91 49 d8	E......t....%......d.?..!.D...I.
0c20	14 19 97 4c 91 4c a0 13 d4 14 25 d8 21 22 a0 03 90 44 98 13 92 49 d8 15 18 98 41 92 58 d8 14 1a	...L.L....%.!"...D...I....A.X...
0c40	97 4d 91 4d a0 31 a0 23 d5 14 26 d8 15 18 a0 05 d2 15 25 d8 19 1d 98 63 99 19 90 42 d8 1d 20 a0	.M.M.1.#..&.......%....c...B....
0c60	21 98 48 90 45 d8 18 1c 98 51 99 07 90 41 d8 1a 1b a0 32 99 2b d8 18 1d 9f 0c 99 0c a0 51 9c 0f	!.H.E....Q...A....2.+........Q..
0c80	d8 1c 20 a0 11 99 47 98 01 f0 05 00 1b 1c a0 32 9a 2b f0 06 00 15 1a 97 4c 91 4c a0 11 94 4f d8	......G........2.+......L.L...O.
0ca0	14 1a 97 4d 91 4d a0 25 d4 14 28 d8 14 18 98 13 91 49 97 4d 91 4d a0 21 d5 14 24 f0 21 10 0d 25	...M.M.%..(......I.M.M.!..$.!..%
0cc0	f2 07 00 0f 14 f0 28 00 15 19 f2 00 01 09 23 88 44 d8 0c 12 8f 4a 89 4a 90 74 98 54 d5 0c 22 f0	......(.......#.D....J.J.t.T..".
0ce0	03 01 09 23 e0 0f 13 88 04 f3 39 00 0b 11 f0 3a 00 0c 12 80 4d f3 00 00 00 00 63 02 00 00 00 00	...#......9....:....M.....c.....
0d00	00 00 00 00 00 00 00 05 00 00 00 23 00 00 00 f3 d2 03 00 00 87 00 87 05 87 06 4b 00 01 00 97 00	...........#..............K.....
0d20	7c 01 81 16 7c 01 64 02 6b 28 00 00 72 01 79 01 7c 01 64 02 6b 02 00 00 72 0b 74 01 00 00 00 00	|...|.d.k(..r.y.|.d.k...r.t.....
0d40	00 00 00 00 64 03 ab 01 00 00 00 00 00 00 82 01 89 00 6a 03 00 00 00 00 00 00 00 00 00 00 00 00	....d.............j.............
0d60	00 00 00 00 00 00 ab 00 00 00 00 00 00 00 7d 02 64 04 84 00 89 00 6a 04 00 00 00 00 00 00 00 00	..............}.d.....j.........
0d80	00 00 00 00 00 00 00 00 00 00 6a 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00	..........j.....................
0da0	00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 45 00 64 01 7b 03 00 00 96 02 97 02 86 05 05 00	......D.........E.d.{...........
0dc0	01 00 7c 01 81 06 7c 01 64 05 6b 28 00 00 72 01 79 01 89 00 6a 09 00 00 00 00 00 00 00 00 00 00	..|...|.d.k(..r.y...j...........
0de0	00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 72 6b 7c 02 73 69 74 0b 00 00 00 00 00 00 00 00	................rk|.sit.........
0e00	ab 00 00 00 00 00 00 00 8a 06 89 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	............j...................
0e20	6a 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 44 00 5d 42	j...........................D.]B
0e40	00 00 5c 02 00 00 8a 05 7d 03 88 06 66 01 64 06 84 08 7c 03 6a 07 00 00 00 00 00 00 00 00 00 00	..\.....}...f.d...|.j...........
0e60	00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 7d 04 88 05 66 01	................D.........}...f.
0e80	64 07 84 08 7c 04 44 00 ab 00 00 00 00 00 00 00 45 00 64 01 7b 03 00 00 96 02 97 02 86 05 05 00	d...|.D.........E.d.{...........
0ea0	01 00 89 06 6a 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 89 05 ab 01 00 00 00 00	....j...........................
0ec0	00 00 01 00 8c 44 04 00 7c 02 72 35 74 0f 00 00 00 00 00 00 00 00 6a 10 00 00 00 00 00 00 00 00	.....D..|.r5t.........j.........
0ee0	00 00 00 00 00 00 00 00 00 00 64 08 84 00 89 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00	..........d.....j...............
0f00	00 00 00 00 6a 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00	....j...........................
0f20	44 00 ab 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 8a 00 6e 34 74 0f 00 00 00 00 00 00 00 00	D...................n4t.........
0f40	6a 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 09 84 00 89 00 6a 04 00 00 00 00	j...................d.....j.....
0f60	00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	..............j.................
0f80	00 00 ab 00 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 8a 00 7c 01	..........D...................|.
0fa0	81 68 7c 01 64 0a 6b 28 00 00 72 63 7c 02 72 60 74 0b 00 00 00 00 00 00 00 00 ab 00 00 00 00 00	.h|.d.k(..rc|.r`t...............
0fc0	00 00 8a 06 89 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 07 00 00 00 00	......j...................j.....
0fe0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 44 00 5d 39 00 00 5c 02 00 00	......................D.]9..\...
1000	8a 05 7d 03 88 00 88 05 66 02 64 0b 84 08 89 06 6a 15 00 00 00 00 00 00 00 00 00 00 00 00 00 00	..}.....f.d.....j...............
1020	00 00 00 00 7c 03 ab 01 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 45 00 64 01 7b 03 00 00	....|.........D.........E.d.{...
1040	96 02 97 02 86 05 05 00 01 00 89 06 6a 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	............j...................
1060	89 05 ab 01 00 00 00 00 00 00 01 00 8c 3b 04 00 79 01 7c 02 72 15 74 17 00 00 00 00 00 00 00 00	.............;..y.|.r.t.........
1080	89 00 7c 01 ab 02 00 00 00 00 00 00 45 00 64 01 7b 03 00 00 96 02 97 02 86 05 05 00 01 00 79 01	..|.........E.d.{.............y.
10a0	74 19 00 00 00 00 00 00 00 00 89 00 7c 01 ab 02 00 00 00 00 00 00 45 00 64 01 7b 03 00 00 96 02	t...........|.........E.d.{.....
10c0	97 02 86 05 05 00 01 00 79 01 37 00 90 01 8c 89 37 00 90 01 8c 1c 37 00 8c 4a 37 00 8c 22 37 00	........y.7.....7.....7..J7.."7.
10e0	8c 0f ad 03 77 01 29 0c 61 b1 0f 00 00 46 69 6e 64 20 73 69 6d 70 6c 65 20 63 79 63 6c 65 73 20	....w.).a....Find.simple.cycles.
1100	28 65 6c 65 6d 65 6e 74 61 72 79 20 63 69 72 63 75 69 74 73 29 20 6f 66 20 61 20 67 72 61 70 68	(elementary.circuits).of.a.graph
1120	2e 0a 0a 20 20 20 20 41 20 22 73 69 6d 70 6c 65 20 63 79 63 6c 65 22 2c 20 6f 72 20 22 65 6c 65	.......A."simple.cycle",.or."ele
1140	6d 65 6e 74 61 72 79 20 63 69 72 63 75 69 74 22 2c 20 69 73 20 61 20 63 6c 6f 73 65 64 20 70 61	mentary.circuit",.is.a.closed.pa
1160	74 68 20 77 68 65 72 65 0a 20 20 20 20 6e 6f 20 6e 6f 64 65 20 61 70 70 65 61 72 73 20 74 77 69	th.where.....no.node.appears.twi
1180	63 65 2e 20 20 49 6e 20 61 20 64 69 72 65 63 74 65 64 20 67 72 61 70 68 2c 20 74 77 6f 20 73 69	ce...In.a.directed.graph,.two.si
11a0	6d 70 6c 65 20 63 79 63 6c 65 73 20 61 72 65 20 64 69 73 74 69 6e 63 74 0a 20 20 20 20 69 66 20	mple.cycles.are.distinct.....if.
11c0	74 68 65 79 20 61 72 65 20 6e 6f 74 20 63 79 63 6c 69 63 20 70 65 72 6d 75 74 61 74 69 6f 6e 73	they.are.not.cyclic.permutations
11e0	20 6f 66 20 65 61 63 68 20 6f 74 68 65 72 2e 20 20 49 6e 20 61 6e 20 75 6e 64 69 72 65 63 74 65	.of.each.other...In.an.undirecte
1200	64 20 67 72 61 70 68 2c 0a 20 20 20 20 74 77 6f 20 73 69 6d 70 6c 65 20 63 79 63 6c 65 73 20 61	d.graph,.....two.simple.cycles.a
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1260	72 20 6e 6f 72 20 6f 66 20 74 68 65 20 6f 74 68 65 72 27 73 20 72 65 76 65 72 73 61 6c 2e 0a 0a	r.nor.of.the.other's.reversal...
1280	20 20 20 20 4f 70 74 69 6f 6e 61 6c 6c 79 2c 20 74 68 65 20 63 79 63 6c 65 73 20 61 72 65 20 62	....Optionally,.the.cycles.are.b
12a0	6f 75 6e 64 65 64 20 69 6e 20 6c 65 6e 67 74 68 2e 20 20 49 6e 20 74 68 65 20 75 6e 62 6f 75 6e	ounded.in.length...In.the.unboun
12c0	64 65 64 20 63 61 73 65 2c 20 77 65 20 75 73 65 0a 20 20 20 20 61 20 6e 6f 6e 72 65 63 75 72 73	ded.case,.we.use.....a.nonrecurs
12e0	69 76 65 2c 20 69 74 65 72 61 74 6f 72 2f 67 65 6e 65 72 61 74 6f 72 20 76 65 72 73 69 6f 6e 20	ive,.iterator/generator.version.
1300	6f 66 20 4a 6f 68 6e 73 6f 6e 27 73 20 61 6c 67 6f 72 69 74 68 6d 20 5b 31 5d 5f 2e 20 20 49 6e	of.Johnson's.algorithm.[1]_...In
1320	0a 20 20 20 20 74 68 65 20 62 6f 75 6e 64 65 64 20 63 61 73 65 2c 20 77 65 20 75 73 65 20 61 20	.....the.bounded.case,.we.use.a.
1340	76 65 72 73 69 6f 6e 20 6f 66 20 74 68 65 20 61 6c 67 6f 72 69 74 68 6d 20 6f 66 20 47 75 70 74	version.of.the.algorithm.of.Gupt
1360	61 20 61 6e 64 0a 20 20 20 20 53 75 7a 75 6d 75 72 61 20 5b 32 5d 5f 2e 20 54 68 65 72 65 20 6d	a.and.....Suzumura.[2]_..There.m
1380	61 79 20 62 65 20 62 65 74 74 65 72 20 61 6c 67 6f 72 69 74 68 6d 73 20 66 6f 72 20 73 6f 6d 65	ay.be.better.algorithms.for.some
13a0	20 63 61 73 65 73 20 5b 33 5d 5f 20 5b 34 5d 5f 20 5b 35 5d 5f 2e 0a 0a 20 20 20 20 54 68 65 20	.cases.[3]_.[4]_.[5]_.......The.
13c0	61 6c 67 6f 72 69 74 68 6d 73 20 6f 66 20 4a 6f 68 6e 73 6f 6e 2c 20 61 6e 64 20 47 75 70 74 61	algorithms.of.Johnson,.and.Gupta
13e0	20 61 6e 64 20 53 75 7a 75 6d 75 72 61 2c 20 61 72 65 20 65 6e 68 61 6e 63 65 64 20 62 79 20 73	.and.Suzumura,.are.enhanced.by.s
1400	6f 6d 65 0a 20 20 20 20 77 65 6c 6c 2d 6b 6e 6f 77 6e 20 70 72 65 70 72 6f 63 65 73 73 69 6e 67	ome.....well-known.preprocessing
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1440	65 64 2c 20 77 65 20 72 65 73 74 72 69 63 74 20 6f 75 72 0a 20 20 20 20 61 74 74 65 6e 74 69 6f	ed,.we.restrict.our.....attentio
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14a0	79 63 6c 65 73 0a 20 20 20 20 63 6f 6e 74 61 69 6e 69 6e 67 20 61 20 63 65 72 74 61 69 6e 20 6e	ycles.....containing.a.certain.n
14c0	6f 64 65 2c 20 72 65 6d 6f 76 65 20 74 68 61 74 20 6e 6f 64 65 2c 20 61 6e 64 20 66 75 72 74 68	ode,.remove.that.node,.and.furth
14e0	65 72 20 64 65 63 6f 6d 70 6f 73 65 20 74 68 65 0a 20 20 20 20 72 65 6d 61 69 6e 64 65 72 20 69	er.decompose.the.....remainder.i
1500	6e 74 6f 20 73 74 72 6f 6e 67 6c 79 20 63 6f 6e 6e 65 63 74 65 64 20 63 6f 6d 70 6f 6e 65 6e 74	nto.strongly.connected.component
1520	73 2e 20 20 57 68 65 6e 20 60 47 60 20 69 73 20 75 6e 64 69 72 65 63 74 65 64 2c 20 77 65 0a 20	s...When.`G`.is.undirected,.we..
1540	20 20 20 72 65 73 74 72 69 63 74 20 6f 75 72 20 61 74 74 65 6e 74 69 6f 6e 20 74 6f 20 62 69 63	...restrict.our.attention.to.bic
1560	6f 6e 6e 65 63 74 65 64 20 63 6f 6d 70 6f 6e 65 6e 74 73 2c 20 67 65 6e 65 72 61 74 65 20 61 6c	onnected.components,.generate.al
1580	6c 20 73 69 6d 70 6c 65 20 63 79 63 6c 65 73 0a 20 20 20 20 63 6f 6e 74 61 69 6e 69 6e 67 20 61	l.simple.cycles.....containing.a
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15c0	67 65 2c 20 61 6e 64 20 66 75 72 74 68 65 72 20 64 65 63 6f 6d 70 6f 73 65 20 74 68 65 0a 20 20	ge,.and.further.decompose.the...
15e0	20 20 72 65 6d 61 69 6e 64 65 72 20 69 6e 74 6f 20 62 69 63 6f 6e 6e 65 63 74 65 64 20 63 6f 6d	..remainder.into.biconnected.com
1600	70 6f 6e 65 6e 74 73 2e 0a 0a 20 20 20 20 4e 6f 74 65 20 74 68 61 74 20 6d 75 6c 74 69 67 72 61	ponents.......Note.that.multigra
1620	70 68 73 20 61 72 65 20 73 75 70 70 6f 72 74 65 64 20 62 79 20 74 68 69 73 20 66 75 6e 63 74 69	phs.are.supported.by.this.functi
1640	6f 6e 20 2d 2d 20 61 6e 64 20 69 6e 20 75 6e 64 69 72 65 63 74 65 64 0a 20 20 20 20 6d 75 6c 74	on.--.and.in.undirected.....mult
1660	69 67 72 61 70 68 73 2c 20 61 20 70 61 69 72 20 6f 66 20 70 61 72 61 6c 6c 65 6c 20 65 64 67 65	igraphs,.a.pair.of.parallel.edge
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16a0	68 20 32 2e 0a 20 20 20 20 4c 69 6b 65 77 69 73 65 2c 20 73 65 6c 66 2d 6c 6f 6f 70 73 20 61 72	h.2......Likewise,.self-loops.ar
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16e0	67 74 68 20 31 2e 20 20 57 65 20 64 65 66 69 6e 65 0a 20 20 20 20 63 79 63 6c 65 73 20 61 73 20	gth.1...We.define.....cycles.as.
1700	73 65 71 75 65 6e 63 65 73 20 6f 66 20 6e 6f 64 65 73 3b 20 73 6f 20 74 68 65 20 70 72 65 73 65	sequences.of.nodes;.so.the.prese
1720	6e 63 65 20 6f 66 20 6c 6f 6f 70 73 20 61 6e 64 20 70 61 72 61 6c 6c 65 6c 20 65 64 67 65 73 0a	nce.of.loops.and.parallel.edges.
1740	20 20 20 20 64 6f 65 73 20 6e 6f 74 20 63 68 61 6e 67 65 20 74 68 65 20 6e 75 6d 62 65 72 20 6f	....does.not.change.the.number.o
1760	66 20 73 69 6d 70 6c 65 20 63 79 63 6c 65 73 20 69 6e 20 61 20 67 72 61 70 68 2e 0a 0a 20 20 20	f.simple.cycles.in.a.graph......
1780	20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47	.Parameters.....----------.....G
17a0	20 3a 20 4e 65 74 77 6f 72 6b 58 20 47 72 61 70 68 0a 20 20 20 20 20 20 20 41 20 6e 65 74 77 6f	.:.NetworkX.Graph........A.netwo
17c0	72 6b 78 20 67 72 61 70 68 2e 20 55 6e 64 69 72 65 63 74 65 64 2c 20 64 69 72 65 63 74 65 64 2c	rkx.graph..Undirected,.directed,
17e0	20 61 6e 64 20 6d 75 6c 74 69 67 72 61 70 68 73 20 61 72 65 20 61 6c 6c 20 73 75 70 70 6f 72 74	.and.multigraphs.are.all.support
1800	65 64 2e 0a 0a 20 20 20 20 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 20 3a 20 69 6e 74 20 6f 72 20 4e	ed.......length_bound.:.int.or.N
1820	6f 6e 65 2c 20 6f 70 74 69 6f 6e 61 6c 20 28 64 65 66 61 75 6c 74 3d 4e 6f 6e 65 29 0a 20 20 20	one,.optional.(default=None)....
1840	20 20 20 20 49 66 20 60 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 60 20 69 73 20 61 6e 20 69 6e 74 2c	....If.`length_bound`.is.an.int,
1860	20 67 65 6e 65 72 61 74 65 20 61 6c 6c 20 73 69 6d 70 6c 65 20 63 79 63 6c 65 73 20 6f 66 20 60	.generate.all.simple.cycles.of.`
1880	47 60 20 77 69 74 68 20 6c 65 6e 67 74 68 20 61 74 0a 20 20 20 20 20 20 20 6d 6f 73 74 20 60 6c	G`.with.length.at........most.`l
18a0	65 6e 67 74 68 5f 62 6f 75 6e 64 60 2e 20 20 4f 74 68 65 72 77 69 73 65 2c 20 67 65 6e 65 72 61	ength_bound`...Otherwise,.genera
18c0	74 65 20 61 6c 6c 20 73 69 6d 70 6c 65 20 63 79 63 6c 65 73 20 6f 66 20 60 47 60 2e 0a 0a 20 20	te.all.simple.cycles.of.`G`.....
18e0	20 20 59 69 65 6c 64 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6c 69 73 74 20 6f 66 20	..Yields.....------.....list.of.
1900	6e 6f 64 65 73 0a 20 20 20 20 20 20 20 45 61 63 68 20 63 79 63 6c 65 20 69 73 20 72 65 70 72 65	nodes........Each.cycle.is.repre
1920	73 65 6e 74 65 64 20 62 79 20 61 20 6c 69 73 74 20 6f 66 20 6e 6f 64 65 73 20 61 6c 6f 6e 67 20	sented.by.a.list.of.nodes.along.
1940	74 68 65 20 63 79 63 6c 65 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d	the.cycle.......Examples.....---
1960	2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 44 69 47 72 61 70 68 28 5b 28 30	-----.....>>>.G.=.nx.DiGraph([(0
1980	2c 20 30 29 2c 20 28 30 2c 20 31 29 2c 20 28 30 2c 20 32 29 2c 20 28 31 2c 20 32 29 2c 20 28 32	,.0),.(0,.1),.(0,.2),.(1,.2),.(2
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19c0	6f 72 74 65 64 28 6e 78 2e 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 28 47 29 29 0a 20 20 20 20 5b	orted(nx.simple_cycles(G)).....[
19e0	5b 30 5d 2c 20 5b 30 2c 20 31 2c 20 32 5d 2c 20 5b 30 2c 20 32 5d 2c 20 5b 31 2c 20 32 5d 2c 20	[0],.[0,.1,.2],.[0,.2],.[1,.2],.
1a00	5b 32 5d 5d 0a 0a 20 20 20 20 54 6f 20 66 69 6c 74 65 72 20 74 68 65 20 63 79 63 6c 65 73 20 73	[2]]......To.filter.the.cycles.s
1a20	6f 20 74 68 61 74 20 74 68 65 79 20 64 6f 6e 27 74 20 69 6e 63 6c 75 64 65 20 63 65 72 74 61 69	o.that.they.don't.include.certai
1a40	6e 20 6e 6f 64 65 73 20 6f 72 20 65 64 67 65 73 2c 0a 20 20 20 20 63 6f 70 79 20 79 6f 75 72 20	n.nodes.or.edges,.....copy.your.
1a60	67 72 61 70 68 20 61 6e 64 20 65 6c 69 6d 69 6e 61 74 65 20 74 68 6f 73 65 20 6e 6f 64 65 73 20	graph.and.eliminate.those.nodes.
1a80	6f 72 20 65 64 67 65 73 20 62 65 66 6f 72 65 20 63 61 6c 6c 69 6e 67 2e 0a 20 20 20 20 46 6f 72	or.edges.before.calling......For
1aa0	20 65 78 61 6d 70 6c 65 2c 20 74 6f 20 65 78 63 6c 75 64 65 20 73 65 6c 66 2d 6c 6f 6f 70 73 20	.example,.to.exclude.self-loops.
1ac0	66 72 6f 6d 20 74 68 65 20 61 62 6f 76 65 20 65 78 61 6d 70 6c 65 3a 0a 0a 20 20 20 20 3e 3e 3e	from.the.above.example:......>>>
1ae0	20 48 20 3d 20 47 2e 63 6f 70 79 28 29 0a 20 20 20 20 3e 3e 3e 20 48 2e 72 65 6d 6f 76 65 5f 65	.H.=.G.copy().....>>>.H.remove_e
1b00	64 67 65 73 5f 66 72 6f 6d 28 6e 78 2e 73 65 6c 66 6c 6f 6f 70 5f 65 64 67 65 73 28 47 29 29 0a	dges_from(nx.selfloop_edges(G)).
1b20	20 20 20 20 3e 3e 3e 20 73 6f 72 74 65 64 28 6e 78 2e 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 28	....>>>.sorted(nx.simple_cycles(
1b40	48 29 29 0a 20 20 20 20 5b 5b 30 2c 20 31 2c 20 32 5d 2c 20 5b 30 2c 20 32 5d 2c 20 5b 31 2c 20	H)).....[[0,.1,.2],.[0,.2],.[1,.
1b60	32 5d 5d 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 57 68 65	2]]......Notes.....-----.....Whe
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1ba0	6d 65 20 63 6f 6d 70 6c 65 78 69 74 79 20 69 73 20 24 4f 28 28 6e 2b 65 29 28 63 2b 31 29 29 24	me.complexity.is.$O((n+e)(c+1))$
1bc0	20 66 6f 72 20 24 6e 24 0a 20 20 20 20 6e 6f 64 65 73 2c 20 24 65 24 20 65 64 67 65 73 20 61 6e	.for.$n$.....nodes,.$e$.edges.an
1be0	64 20 24 63 24 20 73 69 6d 70 6c 65 20 63 69 72 63 75 69 74 73 2e 20 20 4f 74 68 65 72 77 69 73	d.$c$.simple.circuits...Otherwis
1c00	65 2c 20 77 68 65 6e 20 60 60 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 20 3e 20 31 60 60 2c 0a 20 20	e,.when.``length_bound.>.1``,...
1c20	20 20 74 68 65 20 74 69 6d 65 20 63 6f 6d 70 6c 65 78 69 74 79 20 69 73 20 24 4f 28 28 63 2b 6e	..the.time.complexity.is.$O((c+n
1c40	29 28 6b 2d 31 29 64 5e 6b 29 24 20 77 68 65 72 65 20 24 64 24 20 69 73 20 74 68 65 20 61 76 65	)(k-1)d^k)$.where.$d$.is.the.ave
1c60	72 61 67 65 20 64 65 67 72 65 65 20 6f 66 0a 20 20 20 20 74 68 65 20 6e 6f 64 65 73 20 6f 66 20	rage.degree.of.....the.nodes.of.
1c80	60 47 60 20 61 6e 64 20 24 6b 24 20 3d 20 60 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 60 2e 0a 0a 20	`G`.and.$k$.=.`length_bound`....
1ca0	20 20 20 52 61 69 73 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 56 61 6c 75 65 45 72	...Raises.....------.....ValueEr
1cc0	72 6f 72 0a 20 20 20 20 20 20 20 20 77 68 65 6e 20 60 60 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 20	ror.........when.``length_bound.
1ce0	3c 20 30 60 60 2e 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d	<.0``.......References.....-----
1d00	2d 2d 2d 2d 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 46 69 6e 64 69 6e 67 20 61 6c 6c 20 74 68 65	-----........[1].Finding.all.the
1d20	20 65 6c 65 6d 65 6e 74 61 72 79 20 63 69 72 63 75 69 74 73 20 6f 66 20 61 20 64 69 72 65 63 74	.elementary.circuits.of.a.direct
1d40	65 64 20 67 72 61 70 68 2e 0a 20 20 20 20 20 20 20 44 2e 20 42 2e 20 4a 6f 68 6e 73 6f 6e 2c 20	ed.graph.........D..B..Johnson,.
1d60	53 49 41 4d 20 4a 6f 75 72 6e 61 6c 20 6f 6e 20 43 6f 6d 70 75 74 69 6e 67 20 34 2c 20 6e 6f 2e	SIAM.Journal.on.Computing.4,.no.
1d80	20 31 2c 20 37 37 2d 38 34 2c 20 31 39 37 35 2e 0a 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f	.1,.77-84,.1975.........https://
1da0	64 6f 69 2e 6f 72 67 2f 31 30 2e 31 31 33 37 2f 30 32 30 34 30 30 37 0a 20 20 20 20 2e 2e 20 5b	doi.org/10.1137/0204007........[
1dc0	32 5d 20 46 69 6e 64 69 6e 67 20 41 6c 6c 20 42 6f 75 6e 64 65 64 2d 4c 65 6e 67 74 68 20 53 69	2].Finding.All.Bounded-Length.Si
1de0	6d 70 6c 65 20 43 79 63 6c 65 73 20 69 6e 20 61 20 44 69 72 65 63 74 65 64 20 47 72 61 70 68 0a	mple.Cycles.in.a.Directed.Graph.
1e00	20 20 20 20 20 20 20 41 2e 20 47 75 70 74 61 20 61 6e 64 20 54 2e 20 53 75 7a 75 6d 75 72 61 20	.......A..Gupta.and.T..Suzumura.
1e20	68 74 74 70 73 3a 2f 2f 61 72 78 69 76 2e 6f 72 67 2f 61 62 73 2f 32 31 30 35 2e 31 30 30 39 34	https://arxiv.org/abs/2105.10094
1e40	0a 20 20 20 20 2e 2e 20 5b 33 5d 20 45 6e 75 6d 65 72 61 74 69 6e 67 20 74 68 65 20 63 79 63 6c	........[3].Enumerating.the.cycl
1e60	65 73 20 6f 66 20 61 20 64 69 67 72 61 70 68 3a 20 61 20 6e 65 77 20 70 72 65 70 72 6f 63 65 73	es.of.a.digraph:.a.new.preproces
1e80	73 69 6e 67 20 73 74 72 61 74 65 67 79 2e 0a 20 20 20 20 20 20 20 47 2e 20 4c 6f 69 7a 6f 75 20	sing.strategy.........G..Loizou.
1ea0	61 6e 64 20 50 2e 20 54 68 61 6e 69 73 68 2c 20 49 6e 66 6f 72 6d 61 74 69 6f 6e 20 53 63 69 65	and.P..Thanish,.Information.Scie
1ec0	6e 63 65 73 2c 20 76 2e 20 32 37 2c 20 31 36 33 2d 31 38 32 2c 20 31 39 38 32 2e 0a 20 20 20 20	nces,.v..27,.163-182,.1982......
1ee0	2e 2e 20 5b 34 5d 20 41 20 73 65 61 72 63 68 20 73 74 72 61 74 65 67 79 20 66 6f 72 20 74 68 65	...[4].A.search.strategy.for.the
1f00	20 65 6c 65 6d 65 6e 74 61 72 79 20 63 79 63 6c 65 73 20 6f 66 20 61 20 64 69 72 65 63 74 65 64	.elementary.cycles.of.a.directed
1f20	20 67 72 61 70 68 2e 0a 20 20 20 20 20 20 20 4a 2e 4c 2e 20 53 7a 77 61 72 63 66 69 74 65 72 20	.graph.........J.L..Szwarcfiter.
1f40	61 6e 64 20 50 2e 45 2e 20 4c 61 75 65 72 2c 20 42 49 54 20 4e 55 4d 45 52 49 43 41 4c 20 4d 41	and.P.E..Lauer,.BIT.NUMERICAL.MA
1f60	54 48 45 4d 41 54 49 43 53 2c 0a 20 20 20 20 20 20 20 76 2e 20 31 36 2c 20 6e 6f 2e 20 32 2c 20	THEMATICS,........v..16,.no..2,.
1f80	31 39 32 2d 32 30 34 2c 20 31 39 37 36 2e 0a 20 20 20 20 2e 2e 20 5b 35 5d 20 4f 70 74 69 6d 61	192-204,.1976.........[5].Optima
1fa0	6c 20 4c 69 73 74 69 6e 67 20 6f 66 20 43 79 63 6c 65 73 20 61 6e 64 20 73 74 2d 50 61 74 68 73	l.Listing.of.Cycles.and.st-Paths
1fc0	20 69 6e 20 55 6e 64 69 72 65 63 74 65 64 20 47 72 61 70 68 73 0a 20 20 20 20 20 20 20 20 52 2e	.in.Undirected.Graphs.........R.
1fe0	20 46 65 72 72 65 69 72 61 20 61 6e 64 20 52 2e 20 47 72 6f 73 73 69 20 61 6e 64 20 41 2e 20 4d	.Ferreira.and.R..Grossi.and.A..M
2000	61 72 69 6e 6f 20 61 6e 64 20 4e 2e 20 50 69 73 61 6e 74 69 20 61 6e 64 20 52 2e 20 52 69 7a 7a	arino.and.N..Pisanti.and.R..Rizz
2020	69 20 61 6e 64 0a 20 20 20 20 20 20 20 20 47 2e 20 53 61 63 6f 6d 6f 74 6f 20 68 74 74 70 73 3a	i.and.........G..Sacomoto.https:
2040	2f 2f 61 72 78 69 76 2e 6f 72 67 2f 61 62 73 2f 31 32 30 35 2e 32 37 36 36 0a 0a 20 20 20 20 53	//arxiv.org/abs/1205.2766......S
2060	65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 79 63 6c 65 5f 62	ee.Also.....--------.....cycle_b
2080	61 73 69 73 0a 20 20 20 20 63 68 6f 72 64 6c 65 73 73 5f 63 79 63 6c 65 73 0a 20 20 20 20 4e 72	asis.....chordless_cycles.....Nr
20a0	02 00 00 00 fa 21 6c 65 6e 67 74 68 20 62 6f 75 6e 64 20 6d 75 73 74 20 62 65 20 6e 6f 6e 2d 6e	.....!length.bound.must.be.non-n
20c0	65 67 61 74 69 76 65 63 01 00 00 00 00 00 00 00 00 00 00 00 03 00 00 00 33 00 00 00 f3 32 00 00	egativec................3....2..
20e0	00 4b 00 01 00 97 00 7c 00 5d 0f 00 00 5c 02 00 00 7d 01 7d 02 7c 01 7c 02 76 00 73 01 8c 0b 7c	.K.....|.]...\...}.}.|.|.v.s...|
2100	01 67 01 96 01 97 01 01 00 8c 11 04 00 79 00 ad 03 77 01 a9 01 4e a9 00 a9 03 da 02 2e 30 da 01	.g...........y...w...N.......0..
2120	76 da 02 47 76 73 03 00 00 00 20 20 20 72 28 00 00 00 fa 09 3c 67 65 6e 65 78 70 72 3e 7a 20 73	v..Gvs.......r(.....<genexpr>z.s
2140	69 6d 70 6c 65 5f 63 79 63 6c 65 73 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 3e cd	imple_cycles.<locals>.<genexpr>.
2160	00 00 00 73 1c 00 00 00 e8 00 f8 80 00 d2 0f 3a 99 05 98 01 98 32 b0 21 b0 72 b2 27 90 11 94 03	...s...........:.....2.!.r.'....
2180	d1 0f 3a f9 f3 08 00 00 00 82 0c 17 01 8f 08 17 01 e9 01 00 00 00 63 01 00 00 00 00 00 00 00 00	..:...................c.........
21a0	00 00 00 05 00 00 00 33 00 00 00 f3 48 00 00 00 95 01 4b 00 01 00 97 00 7c 00 5d 19 00 00 5c 02	.......3....H.....K.....|.]...\.
21c0	00 00 7d 01 7d 02 7c 01 89 03 76 00 73 01 8c 0b 7c 01 74 01 00 00 00 00 00 00 00 00 7c 02 ab 01	..}.}.|...v.s...|.t.........|...
21e0	00 00 00 00 00 00 66 02 96 01 97 01 01 00 8c 1b 04 00 79 00 ad 03 77 01 72 2d 00 00 00 a9 01 da	......f...........y...w.r-......
2200	03 6c 65 6e a9 04 72 30 00 00 00 72 31 00 00 00 da 03 47 75 76 da 07 76 69 73 69 74 65 64 73 04	.len..r0...r1.....Guv..visiteds.
2220	00 00 00 20 20 20 80 72 28 00 00 00 72 33 00 00 00 7a 20 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73	.......r(...r3...z.simple_cycles
2240	2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 3e d5 00 00 00 73 23 00 00 00 f8 e8 00 f8	.<locals>.<genexpr>....s#.......
2260	80 00 d2 1b 53 a9 66 a8 61 b0 13 c0 61 c8 37 c2 6c 98 51 a4 03 a0 43 a3 08 9c 4d d1 1b 53 f9 f3	....S.f.a...a.7.l.Q...C...M..S..
2280	08 00 00 00 83 0c 22 01 90 12 22 01 63 01 00 00 00 00 00 00 00 00 00 00 00 03 00 00 00 33 00 00	......"...".c................3..
22a0	00 f3 38 00 00 00 95 01 4b 00 01 00 97 00 7c 00 5d 11 00 00 5c 02 00 00 7d 01 7d 02 7c 02 64 00	..8.....K.....|.]...\...}.}.|.d.
22c0	6b 44 00 00 73 01 8c 0c 89 03 7c 01 67 02 96 01 97 01 01 00 8c 13 04 00 79 01 ad 03 77 01 a9 02	kD..s.....|.g...........y...w...
22e0	72 35 00 00 00 4e 72 2e 00 00 00 29 04 72 30 00 00 00 72 31 00 00 00 da 01 6d da 01 75 73 04 00	r5...Nr....).r0...r1.....m..us..
2300	00 00 20 20 20 80 72 28 00 00 00 72 33 00 00 00 7a 20 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 2e	......r(...r3...z.simple_cycles.
2320	3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 3e d6 00 00 00 73 1f 00 00 00 f8 e8 00 f8 80	<locals>.<genexpr>....s.........
2340	00 d2 17 41 a1 34 a0 31 a0 61 b8 31 b8 71 bb 35 98 11 98 41 9c 06 d1 17 41 f9 73 08 00 00 00 83	...A.4.1.a.1.q.5...A....A.s.....
2360	0d 1a 01 91 09 1a 01 63 01 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 33 00 00 00 f3 44 00 00	.......c................3....D..
2380	00 4b 00 01 00 97 00 7c 00 5d 18 00 00 5c 02 00 00 7d 01 7d 02 7c 02 44 00 5d 0e 00 00 7d 03 7c	.K.....|.]...\...}.}.|.D.]...}.|
23a0	03 7c 01 6b 37 00 00 73 01 8c 09 7c 01 7c 03 66 02 96 01 97 01 01 00 8c 10 04 00 8c 1a 04 00 79	.|.k7..s...|.|.f...............y
23c0	00 ad 03 77 01 72 2d 00 00 00 72 2e 00 00 00 a9 04 72 30 00 00 00 72 40 00 00 00 da 02 47 75 72	...w.r-...r......r0...r@.....Gur
23e0	31 00 00 00 73 04 00 00 00 20 20 20 20 72 28 00 00 00 72 33 00 00 00 7a 20 73 69 6d 70 6c 65 5f	1...s........r(...r3...z.simple_
2400	63 79 63 6c 65 73 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 3e db 00 00 00 73 2a 00	cycles.<locals>.<genexpr>....s*.
2420	00 00 e8 00 f8 80 00 d2 16 4f a1 25 a0 21 a0 52 c0 22 d2 16 4f b8 51 c8 01 c8 51 cb 06 98 01 98	.........O.%.!.R."..O.Q...Q.....
2440	31 94 76 d0 16 4f 90 76 d1 16 4f f9 f3 08 00 00 00 82 12 20 01 95 0b 20 01 63 01 00 00 00 00 00	1.v..O.v..O..............c......
2460	00 00 00 00 00 00 04 00 00 00 33 00 00 00 f3 44 00 00 00 4b 00 01 00 97 00 7c 00 5d 18 00 00 5c	..........3....D...K.....|.]...\
2480	02 00 00 7d 01 7d 02 7c 02 44 00 5d 0e 00 00 7d 03 7c 03 7c 01 6b 37 00 00 73 01 8c 09 7c 01 7c	...}.}.|.D.]...}.|.|.k7..s...|.|
24a0	03 66 02 96 01 97 01 01 00 8c 10 04 00 8c 1a 04 00 79 00 ad 03 77 01 72 2d 00 00 00 72 2e 00 00	.f...............y...w.r-...r...
24c0	00 72 42 00 00 00 73 04 00 00 00 20 20 20 20 72 28 00 00 00 72 33 00 00 00 7a 20 73 69 6d 70 6c	.rB...s........r(...r3...z.simpl
24e0	65 5f 63 79 63 6c 65 73 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 3e dd 00 00 00 73	e_cycles.<locals>.<genexpr>....s
2500	2a 00 00 00 e8 00 f8 80 00 d2 14 4d a1 05 a0 01 a0 32 c0 02 d2 14 4d b8 31 c0 61 c8 31 c3 66 90	*..........M.....2....M.1.a.1.f.
2520	61 98 11 94 56 d0 14 4d 90 56 d1 14 4d f9 72 44 00 00 00 e9 02 00 00 00 63 01 00 00 00 00 00 00	a...V..M.V..M.rD........c.......
2540	00 00 00 00 00 05 00 00 00 33 00 00 00 f3 4c 00 00 00 95 02 4b 00 01 00 97 00 7c 00 5d 1b 00 00	.........3....L.....K.....|.]...
2560	7d 01 89 02 6a 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 01 89 03 ab 02 00 00	}...j...................|.......
2580	00 00 00 00 73 01 8c 16 7c 01 89 03 67 02 96 01 97 01 01 00 8c 1d 04 00 79 00 ad 03 77 01 72 2d	....s...|...g...........y...w.r-
25a0	00 00 00 a9 01 da 08 68 61 73 5f 65 64 67 65 29 04 72 30 00 00 00 72 31 00 00 00 72 1a 00 00 00	.......has_edge).r0...r1...r....
25c0	72 40 00 00 00 73 04 00 00 00 20 20 80 80 72 28 00 00 00 72 33 00 00 00 7a 20 73 69 6d 70 6c 65	r@...s........r(...r3...z.simple
25e0	5f 63 79 63 6c 65 73 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 3e e4 00 00 00 73 27	_cycles.<locals>.<genexpr>....s'
2600	00 00 00 f8 e8 00 f8 80 00 f2 00 02 1c 12 d8 1f 20 c0 01 c7 0a c1 0a c8 31 c8 61 d5 40 50 90 51	........................1.a.@P.Q
2620	98 01 94 46 f1 03 02 1c 12 f9 73 08 00 00 00 83 17 24 01 9b 09 24 01 29 0d da 0a 56 61 6c 75 65	...F......s......$...$.)...Value
2640	45 72 72 6f 72 da 0b 69 73 5f 64 69 72 65 63 74 65 64 da 03 61 64 6a da 05 69 74 65 6d 73 da 0d	Error..is_directed..adj..items..
2660	69 73 5f 6d 75 6c 74 69 67 72 61 70 68 72 16 00 00 00 72 19 00 00 00 da 02 6e 78 da 07 44 69 47	is_multigraphr....r......nx..DiG
2680	72 61 70 68 da 05 47 72 61 70 68 da 0c 69 6e 74 65 72 73 65 63 74 69 6f 6e da 16 5f 64 69 72 65	raph..Graph..intersection.._dire
26a0	63 74 65 64 5f 63 79 63 6c 65 5f 73 65 61 72 63 68 da 18 5f 75 6e 64 69 72 65 63 74 65 64 5f 63	cted_cycle_search.._undirected_c
26c0	79 63 6c 65 5f 73 65 61 72 63 68 29 07 72 1a 00 00 00 da 0c 6c 65 6e 67 74 68 5f 62 6f 75 6e 64	ycle_search).r......length_bound
26e0	72 10 00 00 00 72 43 00 00 00 da 0c 6d 75 6c 74 69 70 6c 69 63 69 74 79 72 40 00 00 00 72 3b 00	r....rC.....multiplicityr@...r;.
2700	00 00 73 07 00 00 00 60 20 20 20 20 40 40 72 28 00 00 00 72 0a 00 00 00 72 0a 00 00 00 69 00 00	..s....`....@@r(...r....r....i..
2720	00 73 a6 01 00 00 fa e8 00 f8 80 00 f0 7a 02 00 08 14 d0 07 1f d8 0b 17 98 31 d2 0b 1c d8 0c 12	.s...........z...........1......
2740	d8 0d 19 98 41 d2 0d 1d dc 12 1c d0 1d 40 d3 12 41 d0 0c 41 e0 0f 10 8f 7d 89 7d 8b 7f 80 48 d9	....A........@..A..A....}.}...H.
2760	0f 3a a0 11 a7 15 a1 15 a7 1b a1 1b a3 1d d4 0f 3a d7 04 3a d0 04 3a e0 07 13 d0 07 1f a0 4c b0	.:..............:..:..:.......L.
2780	41 d2 24 35 d8 08 0e e0 07 08 87 7f 81 7f d4 07 18 a1 18 dc 12 15 93 25 88 07 d8 15 16 97 55 91	A.$5...................%......U.
27a0	55 97 5b 91 5b 93 5d f2 00 03 09 1b 89 45 88 41 88 72 db 1b 53 b8 02 bf 08 b9 08 bb 0a d4 1b 53	U.[.[.]......E.A.r..S..........S
27c0	88 4c db 17 41 a8 3c d4 17 41 d7 0c 41 d0 0c 41 d8 0c 13 8f 4b 89 4b 98 01 8d 4e f0 07 03 09 1b	.L..A.<..A..A..A....K.K...N.....
27e0	f1 0c 00 08 10 dc 0c 0e 8f 4a 89 4a d1 16 4f a8 31 af 35 a9 35 af 3b a9 3b ab 3d d4 16 4f d3 0c	.........J.J..O.1.5.5.;.;.=..O..
2800	4f 89 01 e4 0c 0e 8f 48 89 48 d1 14 4d a8 11 af 15 a9 15 af 1b a9 1b ab 1d d4 14 4d d3 0c 4d 88	O......H.H..M..............M..M.
2820	01 f0 06 00 08 14 d0 07 1f a0 4c b0 41 d2 24 35 d9 0b 13 dc 16 19 93 65 88 47 d8 19 1a 9f 15 99	..........L.A.$5.......e.G......
2840	15 9f 1b 99 1b 9b 1d f2 00 04 0d 1f 91 05 90 01 90 32 f4 02 02 1c 12 d8 24 2b d7 24 38 d1 24 38	.................2......$+.$8.$8
2860	b8 12 d3 24 3c f4 03 02 1c 12 f7 00 02 11 12 f0 00 02 11 12 f0 06 00 11 18 97 0b 91 0b 98 41 95	...$<.........................A.
2880	0e f0 09 04 0d 1f f0 0a 00 09 0f e1 07 0f dc 13 29 a8 21 a8 5c d3 13 3a d7 08 3a d1 08 3a e4 13	................).!.\..:..:..:..
28a0	2b a8 41 a8 7c d3 13 3c d7 08 3c d1 08 3c f0 41 01 00 05 3b f9 f0 12 00 0d 42 01 f9 f0 1c 02 11	+.A.|..<..<..<.A...;.....B......
28c0	12 f8 f0 0e 00 09 3b f8 e0 08 3c fa 73 5c 00 00 00 85 41 0d 47 27 01 c1 12 01 47 1b 04 c1 13 41	......;...<.s\....A.G'....G....A
28e0	2f 47 27 01 c3 02 01 47 1e 06 c3 03 43 13 47 27 01 c6 16 01 47 21 06 c6 17 29 47 27 01 c7 00 01	/G'....G....C.G'....G!...)G'....
2900	47 23 04 c7 01 14 47 27 01 c7 15 01 47 25 04 c7 16 06 47 27 01 c7 1e 01 47 27 01 c7 21 01 47 27	G#....G'....G%....G'....G'..!.G'
2920	01 c7 23 01 47 27 01 c7 25 01 47 27 01 63 02 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 23 00	..#.G'..%.G'.c................#.
2940	00 00 f3 b6 01 00 00 4b 00 01 00 97 00 74 00 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00	.......K.....t.........j........
2960	00 00 00 00 00 00 00 00 00 00 00 7d 02 02 00 7c 02 7c 00 ab 01 00 00 00 00 00 00 44 00 8f 03 63	...........}...|.|.........D...c
2980	02 67 00 63 02 5d 13 00 00 7d 03 74 05 00 00 00 00 00 00 00 00 7c 03 ab 01 00 00 00 00 00 00 64	.g.c.]...}.t.........|.........d
29a0	01 6b 5c 00 00 73 01 8c 12 7c 03 91 02 8c 15 04 00 7d 04 7d 03 7c 04 72 96 7c 04 6a 07 00 00 00	.k\..s...|.......}.}.|.r.|.j....
29c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 7d 03 7c 00 6a 09 00 00 00	.......................}.|.j....
29e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 03 ab 01 00 00 00 00 00 00 7d 05 74 0b 00 00 00	...............|.........}.t....
2a00	00 00 00 00 00 74 0d 00 00 00 00 00 00 00 00 7c 03 ab 01 00 00 00 00 00 00 ab 01 00 00 00 00 00	.....t.........|................
2a20	00 7d 06 7c 01 80 16 74 0f 00 00 00 00 00 00 00 00 7c 05 7c 06 67 01 ab 02 00 00 00 00 00 00 45	.}.|...t.........|.|.g.........E
2a40	00 64 02 7b 03 00 00 96 02 97 02 86 05 05 00 01 00 6e 16 74 11 00 00 00 00 00 00 00 00 7c 05 7c	.d.{.............n.t.........|.|
2a60	06 67 01 7c 01 ab 03 00 00 00 00 00 00 45 00 64 02 7b 03 00 00 96 02 97 02 86 05 05 00 01 00 7c	.g.|.........E.d.{.............|
2a80	00 6a 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 06 ab 01 00 00 00 00 00 00 01	.j...................|..........
2aa0	00 7c 04 6a 15 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 03 84 00 02 00 7c 02 7c	.|.j...................d.....|.|
2ac0	05 ab 01 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 01 00 7c 04 72	.........D...................|.r
2ae0	01 8c 95 79 02 79 02 63 02 01 00 63 02 7d 03 77 00 37 00 8c 54 37 00 8c 3f ad 03 77 01 29 04 61	...y.y.c...c.}.w.7..T7..?..w.).a
2b00	ad 04 00 00 41 20 64 69 73 70 61 74 63 68 20 66 75 6e 63 74 69 6f 6e 20 66 6f 72 20 60 73 69 6d	....A.dispatch.function.for.`sim
2b20	70 6c 65 5f 63 79 63 6c 65 73 60 20 66 6f 72 20 64 69 72 65 63 74 65 64 20 67 72 61 70 68 73 2e	ple_cycles`.for.directed.graphs.
2b40	0a 0a 20 20 20 20 57 65 20 67 65 6e 65 72 61 74 65 20 61 6c 6c 20 63 79 63 6c 65 73 20 6f 66 20	......We.generate.all.cycles.of.
2b60	47 20 74 68 72 6f 75 67 68 20 62 69 6e 61 72 79 20 70 61 72 74 69 74 69 6f 6e 2e 0a 0a 20 20 20	G.through.binary.partition......
2b80	20 20 20 20 20 31 2e 20 50 69 63 6b 20 61 20 6e 6f 64 65 20 76 20 69 6e 20 47 20 77 68 69 63 68	.....1..Pick.a.node.v.in.G.which
2ba0	20 62 65 6c 6f 6e 67 73 20 74 6f 20 61 74 20 6c 65 61 73 74 20 6f 6e 65 20 63 79 63 6c 65 0a 20	.belongs.to.at.least.one.cycle..
2bc0	20 20 20 20 20 20 20 20 20 20 20 61 2e 20 47 65 6e 65 72 61 74 65 20 61 6c 6c 20 63 79 63 6c 65	...........a..Generate.all.cycle
2be0	73 20 6f 66 20 47 20 77 68 69 63 68 20 63 6f 6e 74 61 69 6e 20 74 68 65 20 6e 6f 64 65 20 76 2e	s.of.G.which.contain.the.node.v.
2c00	0a 20 20 20 20 20 20 20 20 20 20 20 20 62 2e 20 52 65 63 75 72 73 69 76 65 6c 79 20 67 65 6e 65	.............b..Recursively.gene
2c20	72 61 74 65 20 61 6c 6c 20 63 79 63 6c 65 73 20 6f 66 20 47 20 5c 20 76 2e 0a 0a 20 20 20 20 54	rate.all.cycles.of.G.\.v.......T
2c40	68 69 73 20 69 73 20 61 63 63 6f 6d 70 6c 69 73 68 65 64 20 74 68 72 6f 75 67 68 20 74 68 65 20	his.is.accomplished.through.the.
2c60	66 6f 6c 6c 6f 77 69 6e 67 3a 0a 0a 20 20 20 20 20 20 20 20 31 2e 20 43 6f 6d 70 75 74 65 20 74	following:..........1..Compute.t
2c80	68 65 20 73 74 72 6f 6e 67 6c 79 20 63 6f 6e 6e 65 63 74 65 64 20 63 6f 6d 70 6f 6e 65 6e 74 73	he.strongly.connected.components
2ca0	20 53 43 43 20 6f 66 20 47 2e 0a 20 20 20 20 20 20 20 20 32 2e 20 53 65 6c 65 63 74 20 61 6e 64	.SCC.of.G..........2..Select.and
2cc0	20 72 65 6d 6f 76 65 20 61 20 62 69 63 6f 6e 6e 65 63 74 65 64 20 63 6f 6d 70 6f 6e 65 6e 74 20	.remove.a.biconnected.component.
2ce0	43 20 66 72 6f 6d 20 42 43 43 2e 20 20 53 65 6c 65 63 74 20 61 0a 20 20 20 20 20 20 20 20 20 20	C.from.BCC...Select.a...........
2d00	20 6e 6f 6e 2d 74 72 65 65 20 65 64 67 65 20 28 75 2c 20 76 29 20 6f 66 20 61 20 64 65 70 74 68	.non-tree.edge.(u,.v).of.a.depth
2d20	2d 66 69 72 73 74 20 73 65 61 72 63 68 20 6f 66 20 47 5b 43 5d 2e 0a 20 20 20 20 20 20 20 20 33	-first.search.of.G[C]..........3
2d40	2e 20 46 6f 72 20 65 61 63 68 20 73 69 6d 70 6c 65 20 63 79 63 6c 65 20 50 20 63 6f 6e 74 61 69	..For.each.simple.cycle.P.contai
2d60	6e 69 6e 67 20 76 20 69 6e 20 47 5b 43 5d 2c 20 79 69 65 6c 64 20 50 2e 0a 20 20 20 20 20 20 20	ning.v.in.G[C],.yield.P.........
2d80	20 34 2e 20 41 64 64 20 74 68 65 20 62 69 63 6f 6e 6e 65 63 74 65 64 20 63 6f 6d 70 6f 6e 65 6e	.4..Add.the.biconnected.componen
2da0	74 73 20 6f 66 20 47 5b 43 20 5c 20 76 5d 20 74 6f 20 42 43 43 2e 0a 0a 20 20 20 20 49 66 20 74	ts.of.G[C.\.v].to.BCC.......If.t
2dc0	68 65 20 70 61 72 61 6d 65 74 65 72 20 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 20 69 73 20 6e 6f 74	he.parameter.length_bound.is.not
2de0	20 4e 6f 6e 65 2c 20 74 68 65 6e 20 73 74 65 70 20 33 20 77 69 6c 6c 20 62 65 20 6c 69 6d 69 74	.None,.then.step.3.will.be.limit
2e00	65 64 20 74 6f 0a 20 20 20 20 73 69 6d 70 6c 65 20 63 79 63 6c 65 73 20 6f 66 20 6c 65 6e 67 74	ed.to.....simple.cycles.of.lengt
2e20	68 20 61 74 20 6d 6f 73 74 20 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 2e 0a 0a 20 20 20 20 50 61 72	h.at.most.length_bound.......Par
2e40	61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 20 3a 20 4e	ameters.....----------.....G.:.N
2e60	65 74 77 6f 72 6b 58 20 44 69 47 72 61 70 68 0a 20 20 20 20 20 20 20 41 20 64 69 72 65 63 74 65	etworkX.DiGraph........A.directe
2e80	64 20 67 72 61 70 68 0a 0a 20 20 20 20 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 20 3a 20 69 6e 74 20	d.graph......length_bound.:.int.
2ea0	6f 72 20 4e 6f 6e 65 0a 20 20 20 20 20 20 20 49 66 20 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 20 69	or.None........If.length_bound.i
2ec0	73 20 61 6e 20 69 6e 74 2c 20 67 65 6e 65 72 61 74 65 20 61 6c 6c 20 73 69 6d 70 6c 65 20 63 79	s.an.int,.generate.all.simple.cy
2ee0	63 6c 65 73 20 6f 66 20 47 20 77 69 74 68 20 6c 65 6e 67 74 68 20 61 74 20 6d 6f 73 74 20 6c 65	cles.of.G.with.length.at.most.le
2f00	6e 67 74 68 5f 62 6f 75 6e 64 2e 0a 20 20 20 20 20 20 20 4f 74 68 65 72 77 69 73 65 2c 20 67 65	ngth_bound.........Otherwise,.ge
2f20	6e 65 72 61 74 65 20 61 6c 6c 20 73 69 6d 70 6c 65 20 63 79 63 6c 65 73 20 6f 66 20 47 2e 0a 0a	nerate.all.simple.cycles.of.G...
2f40	20 20 20 20 59 69 65 6c 64 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6c 69 73 74 20 6f	....Yields.....------.....list.o
2f60	66 20 6e 6f 64 65 73 0a 20 20 20 20 20 20 20 45 61 63 68 20 63 79 63 6c 65 20 69 73 20 72 65 70	f.nodes........Each.cycle.is.rep
2f80	72 65 73 65 6e 74 65 64 20 62 79 20 61 20 6c 69 73 74 20 6f 66 20 6e 6f 64 65 73 20 61 6c 6f 6e	resented.by.a.list.of.nodes.alon
2fa0	67 20 74 68 65 20 63 79 63 6c 65 2e 0a 20 20 20 20 72 46 00 00 00 4e 63 01 00 00 00 00 00 00 00	g.the.cycle......rF...Nc........
2fc0	00 00 00 00 04 00 00 00 33 00 00 00 f3 3e 00 00 00 4b 00 01 00 97 00 7c 00 5d 15 00 00 7d 01 74	........3....>...K.....|.]...}.t
2fe0	01 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 64 00 6b 5c 00 00 73 01 8c 12 7c 01 96	.........|.........d.k\..s...|..
3000	01 97 01 01 00 8c 17 04 00 79 01 ad 03 77 01 a9 02 72 46 00 00 00 4e 72 37 00 00 00 a9 02 72 30	.........y...w...rF...Nr7.....r0
3020	00 00 00 da 01 63 73 02 00 00 00 20 20 72 28 00 00 00 72 33 00 00 00 7a 29 5f 64 69 72 65 63 74	.....cs......r(...r3...z)_direct
3040	65 64 5f 63 79 63 6c 65 5f 73 65 61 72 63 68 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70	ed_cycle_search.<locals>.<genexp
3060	72 3e 1f 01 00 00 f3 1a 00 00 00 e8 00 f8 80 00 d2 19 3c a0 01 b4 03 b0 41 b3 06 b8 21 b3 0b 9c	r>................<.....A...!...
3080	21 d1 19 3c f9 f3 08 00 00 00 82 13 1d 01 96 07 1d 01 29 0b 72 4f 00 00 00 da 1d 73 74 72 6f 6e	!..<..............).rO.....stron
30a0	67 6c 79 5f 63 6f 6e 6e 65 63 74 65 64 5f 63 6f 6d 70 6f 6e 65 6e 74 73 72 38 00 00 00 72 17 00	gly_connected_componentsr8...r..
30c0	00 00 da 08 73 75 62 67 72 61 70 68 da 04 6e 65 78 74 da 04 69 74 65 72 da 15 5f 6a 6f 68 6e 73	....subgraph..next..iter.._johns
30e0	6f 6e 5f 63 79 63 6c 65 5f 73 65 61 72 63 68 da 15 5f 62 6f 75 6e 64 65 64 5f 63 79 63 6c 65 5f	on_cycle_search.._bounded_cycle_
3100	73 65 61 72 63 68 da 0b 72 65 6d 6f 76 65 5f 6e 6f 64 65 da 06 65 78 74 65 6e 64 29 07 72 1a 00	search..remove_node..extend).r..
3120	00 00 72 55 00 00 00 da 03 73 63 63 72 5b 00 00 00 da 0a 63 6f 6d 70 6f 6e 65 6e 74 73 da 02 47	..rU.....sccr[.....components..G
3140	63 72 31 00 00 00 73 07 00 00 00 20 20 20 20 20 20 20 72 28 00 00 00 72 53 00 00 00 72 53 00 00	cr1...s...........r(...rS...rS..
3160	00 f0 00 00 00 73 c1 00 00 00 e8 00 f8 80 00 f4 46 01 00 0b 0d d7 0a 2a d1 0a 2a 80 43 d9 1d 20	.....s..........F......*..*.C...
3180	a0 11 9b 56 d6 11 33 98 01 a4 73 a8 31 a3 76 b0 11 a3 7b 92 21 d0 11 33 80 4a d0 11 33 d9 0a 14	...V..3...s.1.v...{.!..3.J..3...
31a0	d8 0c 16 8f 4e 89 4e d3 0c 1c 88 01 d8 0d 0e 8f 5a 89 5a 98 01 8b 5d 88 02 dc 0c 10 94 14 90 61	....N.N.........Z.Z...]........a
31c0	93 17 8b 4d 88 01 d8 0b 17 d0 0b 1f dc 17 2c a8 52 b0 21 b0 13 d3 17 35 d7 0c 35 d1 0c 35 e4 17	...M..........,.R.!....5..5..5..
31e0	2c a8 52 b0 21 b0 13 b0 6c d3 17 43 d7 0c 43 d0 0c 43 e0 08 09 8f 0d 89 0d 90 61 d4 08 18 d8 08	,.R.!...l..C..C..C........a.....
3200	12 d7 08 19 d1 08 19 d1 19 3c a1 53 a8 12 a3 57 d4 19 3c d4 08 3c f4 15 00 0b 15 f9 f2 03 00 12	.........<.S...W..<..<..........
3220	34 f0 0c 00 0d 36 f8 e0 0c 43 fa 73 39 00 00 00 82 1b 43 19 01 9d 13 43 10 04 b1 04 43 10 04 b5	4....6...C.s9.....C....C....C...
3240	41 0b 43 19 01 c2 00 01 43 15 04 c2 01 16 43 19 01 c2 17 01 43 17 04 c2 18 35 43 19 01 c3 0e 08	A.C.....C.....C.....C....5C.....
3260	43 19 01 c3 17 01 43 19 01 63 02 00 00 00 00 00 00 00 00 00 00 00 07 00 00 00 23 00 00 00 f3 d4	C.....C..c................#.....
3280	01 00 00 4b 00 01 00 97 00 74 00 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00	...K.....t.........j............
32a0	00 00 00 00 00 00 00 7d 02 02 00 7c 02 7c 00 ab 01 00 00 00 00 00 00 44 00 8f 03 63 02 67 00 63	.......}...|.|.........D...c.g.c
32c0	02 5d 13 00 00 7d 03 74 05 00 00 00 00 00 00 00 00 7c 03 ab 01 00 00 00 00 00 00 64 01 6b 5c 00	.]...}.t.........|.........d.k\.
32e0	00 73 01 8c 12 7c 03 91 02 8c 15 04 00 7d 04 7d 03 7c 04 72 a5 7c 04 6a 07 00 00 00 00 00 00 00	.s...|.......}.}.|.r.|.j........
3300	00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 7d 03 7c 00 6a 09 00 00 00 00 00 00 00	...................}.|.j........
3320	00 00 00 00 00 00 00 00 00 00 00 7c 03 ab 01 00 00 00 00 00 00 7d 05 74 0b 00 00 00 00 00 00 00	...........|.........}.t........
3340	00 74 0d 00 00 00 00 00 00 00 00 74 0f 00 00 00 00 00 00 00 00 7c 05 6a 10 00 00 00 00 00 00 00	.t.........t.........|.j........
3360	00 00 00 00 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 ab 01 00 00 00	................................
3380	00 00 00 7d 06 02 00 7c 00 6a 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 06 8e	...}...|.j...................|..
33a0	00 01 00 7c 01 80 15 74 15 00 00 00 00 00 00 00 00 7c 05 7c 06 ab 02 00 00 00 00 00 00 45 00 64	...|...t.........|.|.........E.d
33c0	02 7b 03 00 00 96 02 97 02 86 05 05 00 01 00 6e 15 74 17 00 00 00 00 00 00 00 00 7c 05 7c 06 7c	.{.............n.t.........|.|.|
33e0	01 ab 03 00 00 00 00 00 00 45 00 64 02 7b 03 00 00 96 02 97 02 86 05 05 00 01 00 7c 04 6a 19 00	.........E.d.{.............|.j..
3400	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 03 84 00 02 00 7c 02 7c 05 ab 01 00 00 00	.................d.....|.|......
3420	00 00 00 44 00 ab 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 01 00 7c 04 72 01 8c a4 79 02 79	...D...................|.r...y.y
3440	02 63 02 01 00 63 02 7d 03 77 00 37 00 8c 42 37 00 8c 2e ad 03 77 01 29 04 61 c2 04 00 00 41 20	.c...c.}.w.7..B7.....w.).a....A.
3460	64 69 73 70 61 74 63 68 20 66 75 6e 63 74 69 6f 6e 20 66 6f 72 20 60 73 69 6d 70 6c 65 5f 63 79	dispatch.function.for.`simple_cy
3480	63 6c 65 73 60 20 66 6f 72 20 75 6e 64 69 72 65 63 74 65 64 20 67 72 61 70 68 73 2e 0a 0a 20 20	cles`.for.undirected.graphs.....
34a0	20 20 57 65 20 67 65 6e 65 72 61 74 65 20 61 6c 6c 20 63 79 63 6c 65 73 20 6f 66 20 47 20 74 68	..We.generate.all.cycles.of.G.th
34c0	72 6f 75 67 68 20 62 69 6e 61 72 79 20 70 61 72 74 69 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20	rough.binary.partition..........
34e0	20 31 2e 20 50 69 63 6b 20 61 6e 20 65 64 67 65 20 28 75 2c 20 76 29 20 69 6e 20 47 20 77 68 69	.1..Pick.an.edge.(u,.v).in.G.whi
3500	63 68 20 62 65 6c 6f 6e 67 73 20 74 6f 20 61 74 20 6c 65 61 73 74 20 6f 6e 65 20 63 79 63 6c 65	ch.belongs.to.at.least.one.cycle
3520	0a 20 20 20 20 20 20 20 20 20 20 20 20 61 2e 20 47 65 6e 65 72 61 74 65 20 61 6c 6c 20 63 79 63	.............a..Generate.all.cyc
3540	6c 65 73 20 6f 66 20 47 20 77 68 69 63 68 20 63 6f 6e 74 61 69 6e 20 74 68 65 20 65 64 67 65 20	les.of.G.which.contain.the.edge.
3560	28 75 2c 20 76 29 0a 20 20 20 20 20 20 20 20 20 20 20 20 62 2e 20 52 65 63 75 72 73 69 76 65 6c	(u,.v).............b..Recursivel
3580	79 20 67 65 6e 65 72 61 74 65 20 61 6c 6c 20 63 79 63 6c 65 73 20 6f 66 20 47 20 5c 20 28 75 2c	y.generate.all.cycles.of.G.\.(u,
35a0	20 76 29 0a 0a 20 20 20 20 54 68 69 73 20 69 73 20 61 63 63 6f 6d 70 6c 69 73 68 65 64 20 74 68	.v)......This.is.accomplished.th
35c0	72 6f 75 67 68 20 74 68 65 20 66 6f 6c 6c 6f 77 69 6e 67 3a 0a 0a 20 20 20 20 20 20 20 20 31 2e	rough.the.following:..........1.
35e0	20 43 6f 6d 70 75 74 65 20 74 68 65 20 62 69 63 6f 6e 6e 65 63 74 65 64 20 63 6f 6d 70 6f 6e 65	.Compute.the.biconnected.compone
3600	6e 74 73 20 42 43 43 20 6f 66 20 47 2e 0a 20 20 20 20 20 20 20 20 32 2e 20 53 65 6c 65 63 74 20	nts.BCC.of.G..........2..Select.
3620	61 6e 64 20 72 65 6d 6f 76 65 20 61 20 62 69 63 6f 6e 6e 65 63 74 65 64 20 63 6f 6d 70 6f 6e 65	and.remove.a.biconnected.compone
3640	6e 74 20 43 20 66 72 6f 6d 20 42 43 43 2e 20 20 53 65 6c 65 63 74 20 61 0a 20 20 20 20 20 20 20	nt.C.from.BCC...Select.a........
3660	20 20 20 20 6e 6f 6e 2d 74 72 65 65 20 65 64 67 65 20 28 75 2c 20 76 29 20 6f 66 20 61 20 64 65	....non-tree.edge.(u,.v).of.a.de
3680	70 74 68 2d 66 69 72 73 74 20 73 65 61 72 63 68 20 6f 66 20 47 5b 43 5d 2e 0a 20 20 20 20 20 20	pth-first.search.of.G[C]........
36a0	20 20 33 2e 20 46 6f 72 20 65 61 63 68 20 28 76 20 2d 3e 20 75 29 20 70 61 74 68 20 50 20 72 65	..3..For.each.(v.->.u).path.P.re
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36e0	50 2e 0a 20 20 20 20 20 20 20 20 34 2e 20 41 64 64 20 74 68 65 20 62 69 63 6f 6e 6e 65 63 74 65	P..........4..Add.the.biconnecte
3700	64 20 63 6f 6d 70 6f 6e 65 6e 74 73 20 6f 66 20 47 5b 43 5d 20 5c 20 28 75 2c 20 76 29 20 74 6f	d.components.of.G[C].\.(u,.v).to
3720	20 42 43 43 2e 0a 0a 20 20 20 20 49 66 20 74 68 65 20 70 61 72 61 6d 65 74 65 72 20 6c 65 6e 67	.BCC.......If.the.parameter.leng
3740	74 68 5f 62 6f 75 6e 64 20 69 73 20 6e 6f 74 20 4e 6f 6e 65 2c 20 74 68 65 6e 20 73 74 65 70 20	th_bound.is.not.None,.then.step.
3760	33 20 77 69 6c 6c 20 62 65 20 6c 69 6d 69 74 65 64 20 74 6f 20 73 69 6d 70 6c 65 20 70 61 74 68	3.will.be.limited.to.simple.path
3780	73 0a 20 20 20 20 6f 66 20 6c 65 6e 67 74 68 20 61 74 20 6d 6f 73 74 20 6c 65 6e 67 74 68 5f 62	s.....of.length.at.most.length_b
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3880	20 20 4f 74 68 65 72 77 69 73 65 2c 20 67 65 6e 65 72 61 74 65 20 61 6c 6c 20 73 69 6d 70 6c 65	..Otherwise,.generate.all.simple
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38c0	2d 2d 2d 2d 0a 20 20 20 20 6c 69 73 74 20 6f 66 20 6e 6f 64 65 73 0a 20 20 20 20 20 20 20 45 61	----.....list.of.nodes........Ea
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3920	e9 03 00 00 00 4e 63 01 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 33 00 00 00 f3 3e 00 00 00	.....Nc................3....>...
3940	4b 00 01 00 97 00 7c 00 5d 15 00 00 7d 01 74 01 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00	K.....|.]...}.t.........|.......
3960	00 00 64 00 6b 5c 00 00 73 01 8c 12 7c 01 96 01 97 01 01 00 8c 17 04 00 79 01 ad 03 77 01 29 02	..d.k\..s...|...........y...w.).
3980	72 6a 00 00 00 4e 72 37 00 00 00 72 5a 00 00 00 73 02 00 00 00 20 20 72 28 00 00 00 72 33 00 00	rj...Nr7...rZ...s......r(...r3..
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39e0	00 00 00 da 16 62 69 63 6f 6e 6e 65 63 74 65 64 5f 63 6f 6d 70 6f 6e 65 6e 74 73 72 38 00 00 00	.....biconnected_componentsr8...
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3a40	1a 00 00 00 72 55 00 00 00 da 03 62 63 63 72 5b 00 00 00 72 67 00 00 00 72 68 00 00 00 da 02 75	....rU.....bccr[...rg...rh.....u
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3ae0	48 93 7e d3 12 26 d3 0d 27 88 02 d8 08 15 88 01 8f 0d 89 0d 90 72 d1 08 1a e0 0b 17 d0 0b 1f dc	H.~..&..'............r..........
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3b80	c3 1d 08 43 28 01 c3 26 01 43 28 01 63 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00	...C(..&.C(.c...................
3ba0	00 f3 1c 00 00 00 97 00 65 00 5a 01 64 00 5a 02 64 01 5a 03 64 02 84 00 5a 04 64 03 84 00 5a 05	........e.Z.d.Z.d.Z.d...Z.d...Z.
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3c20	0a 20 20 20 20 54 68 69 73 20 64 69 63 74 20 73 75 62 63 6c 61 73 73 20 75 73 65 73 20 74 68 65	.....This.dict.subclass.uses.the
3c40	20 5f 5f 6d 69 73 73 69 6e 67 5f 5f 20 66 75 6e 63 74 69 6f 6e 61 6c 69 74 79 20 74 6f 20 71 75	.__missing__.functionality.to.qu
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3ca0	61 20 6c 69 73 74 2e 20 20 54 68 69 73 20 69 73 20 75 73 65 64 20 74 6f 20 61 76 6f 69 64 0a 20	a.list...This.is.used.to.avoid..
3cc0	20 20 20 74 68 65 20 70 65 72 66 6f 72 6d 61 6e 63 65 20 70 65 6e 61 6c 74 79 20 69 6e 63 75 72	...the.performance.penalty.incur
3ce0	72 65 64 20 62 79 20 73 75 62 67 72 61 70 68 20 76 69 65 77 73 2e 0a 20 20 20 20 63 02 00 00 00	red.by.subgraph.views......c....
3d00	00 00 00 00 00 00 00 00 02 00 00 00 03 00 00 00 f3 12 00 00 00 97 00 7c 01 7c 00 5f 00 00 00 00	.......................|.|._....
3d20	00 00 00 00 00 79 00 72 2d 00 00 00 29 01 72 1a 00 00 00 29 02 da 04 73 65 6c 66 72 1a 00 00 00	.....y.r-...).r....)...selfr....
3d40	73 02 00 00 00 20 20 72 28 00 00 00 da 08 5f 5f 69 6e 69 74 5f 5f 7a 1b 5f 4e 65 69 67 68 62 6f	s......r(.....__init__z._Neighbo
3d60	72 68 6f 6f 64 43 61 63 68 65 2e 5f 5f 69 6e 69 74 5f 5f 5c 01 00 00 73 09 00 00 00 80 00 d8 11	rhoodCache.__init__\...s........
3d80	12 88 04 8d 06 72 29 00 00 00 63 02 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 03 00 00 00 f3	.....r)...c.....................
3da0	40 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 7c 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00	@.....t.........|.j.............
3dc0	00 00 00 00 00 00 7c 01 19 00 00 00 ab 01 00 00 00 00 00 00 78 01 7d 02 7c 00 7c 01 3c 00 00 00	......|.............x.}.|.|.<...
3de0	7c 02 53 00 72 2d 00 00 00 29 02 72 6d 00 00 00 72 1a 00 00 00 29 03 72 75 00 00 00 72 31 00 00	|.S.r-...).rm...r....).ru...r1..
3e00	00 72 32 00 00 00 73 03 00 00 00 20 20 20 72 28 00 00 00 da 0b 5f 5f 6d 69 73 73 69 6e 67 5f 5f	.r2...s.......r(.....__missing__
3e20	7a 1e 5f 4e 65 69 67 68 62 6f 72 68 6f 6f 64 43 61 63 68 65 2e 5f 5f 6d 69 73 73 69 6e 67 5f 5f	z._NeighborhoodCache.__missing__
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3ee0	00 72 73 00 00 00 63 02 00 00 00 00 00 00 00 00 00 00 00 07 00 00 00 23 00 00 00 f3 d6 02 00 00	.rs...c................#........
3f00	4b 00 01 00 97 00 74 01 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 7d 00 74 03 00 00	K.....t.........|.........}.t...
3f20	00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 7d 02 74 05 00 00 00 00 00 00 00 00 74 02 00 00	......|.........}.t.........t...
3f40	00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7d 03 7c 01 64 01 19 00 00 00 7d 04 74 07 00 00 00 00	..............}.|.d.....}.t.....
3f60	00 00 00 00 7c 00 7c 01 64 02 19 00 00 00 19 00 00 00 ab 01 00 00 00 00 00 00 67 01 7d 05 64 03	....|.|.d.................g.}.d.
3f80	67 01 7d 06 7c 05 90 01 72 23 7c 05 64 02 19 00 00 00 7d 07 7c 07 44 00 5d 6a 00 00 7d 08 7c 08	g.}.|...r#|.d.....}.|.D.]j..}.|.
3fa0	7c 04 6b 28 00 00 72 0d 7c 01 64 04 64 04 1a 00 96 01 97 01 01 00 64 05 7c 06 64 02 3c 00 00 00	|.k(..r.|.d.d.........d.|.d.<...
3fc0	8c 15 7c 08 7c 02 76 01 73 01 8c 1a 7c 01 6a 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	..|.|.v.s...|.j.................
3fe0	00 00 7c 08 ab 01 00 00 00 00 00 00 01 00 7c 06 6a 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00	..|...........|.j...............
4000	00 00 00 00 64 03 ab 01 00 00 00 00 00 00 01 00 7c 05 6a 09 00 00 00 00 00 00 00 00 00 00 00 00	....d...........|.j.............
4020	00 00 00 00 00 00 74 07 00 00 00 00 00 00 00 00 7c 00 7c 08 19 00 00 00 ab 01 00 00 00 00 00 00	......t.........|.|.............
4040	ab 01 00 00 00 00 00 00 01 00 7c 02 6a 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	..........|.j...................
4060	7c 08 ab 01 00 00 00 00 00 00 01 00 01 00 6e ab 04 00 7c 05 6a 0d 00 00 00 00 00 00 00 00 00 00	|.............n...|.j...........
4080	00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 01 00 7c 01 6a 0d 00 00 00 00 00 00 00 00 00 00	..................|.j...........
40a0	00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 7d 09 7c 06 6a 0d 00 00 00 00 00 00 00 00 00 00	................}.|.j...........
40c0	00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 72 5c 7c 06 72 05 64 05 7c 06 64 02 3c 00 00 00	................r\|.r.d.|.d.<...
40e0	7c 09 68 01 7d 0a 7c 0a 72 6e 7c 0a 6a 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	|.h.}.|.rn|.j...................
4100	ab 00 00 00 00 00 00 00 7d 0b 7c 0b 7c 02 76 00 72 38 7c 02 6a 0f 00 00 00 00 00 00 00 00 00 00	........}.|.|.v.r8|.j...........
4120	00 00 00 00 00 00 00 00 7c 0b ab 01 00 00 00 00 00 00 01 00 7c 0a 6a 11 00 00 00 00 00 00 00 00	........|...........|.j.........
4140	00 00 00 00 00 00 00 00 00 00 7c 03 7c 0b 19 00 00 00 ab 01 00 00 00 00 00 00 01 00 7c 03 7c 0b	..........|.|...............|.|.
4160	19 00 00 00 6a 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00	....j...........................
4180	01 00 7c 0a 72 01 8c 4f 6e 1e 7c 00 7c 09 19 00 00 00 44 00 5d 16 00 00 7d 08 7c 03 7c 08 19 00	..|.r..On.|.|.....D.]...}.|.|...
41a0	00 00 6a 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 09 ab 01 00 00 00 00 00 00	..j...................|.........
41c0	01 00 8c 18 04 00 7c 05 72 02 90 01 8c 22 79 04 79 04 ad 03 77 01 29 06 61 30 02 00 00 54 68 65	......|.r...."y.y...w.).a0...The
41e0	20 6d 61 69 6e 20 6c 6f 6f 70 20 6f 66 20 74 68 65 20 63 79 63 6c 65 2d 65 6e 75 6d 65 72 61 74	.main.loop.of.the.cycle-enumerat
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4220	61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 20 3a	arameters.....----------.....G.:
4240	20 4e 65 74 77 6f 72 6b 58 20 47 72 61 70 68 20 6f 72 20 44 69 47 72 61 70 68 0a 20 20 20 20 20	.NetworkX.Graph.or.DiGraph......
4260	20 20 41 20 67 72 61 70 68 0a 0a 20 20 20 20 70 61 74 68 20 3a 20 6c 69 73 74 0a 20 20 20 20 20	..A.graph......path.:.list......
4280	20 20 41 20 63 79 63 6c 65 20 70 72 65 66 69 78 2e 20 20 41 6c 6c 20 63 79 63 6c 65 73 20 67 65	..A.cycle.prefix...All.cycles.ge
42a0	6e 65 72 61 74 65 64 20 77 69 6c 6c 20 62 65 67 69 6e 20 77 69 74 68 20 74 68 69 73 20 70 72 65	nerated.will.begin.with.this.pre
42c0	66 69 78 2e 0a 0a 20 20 20 20 59 69 65 6c 64 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20	fix.......Yields.....------.....
42e0	6c 69 73 74 20 6f 66 20 6e 6f 64 65 73 0a 20 20 20 20 20 20 20 45 61 63 68 20 63 79 63 6c 65 20	list.of.nodes........Each.cycle.
4300	69 73 20 72 65 70 72 65 73 65 6e 74 65 64 20 62 79 20 61 20 6c 69 73 74 20 6f 66 20 6e 6f 64 65	is.represented.by.a.list.of.node
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4360	20 46 69 6e 64 69 6e 67 20 61 6c 6c 20 74 68 65 20 65 6c 65 6d 65 6e 74 61 72 79 20 63 69 72 63	.Finding.all.the.elementary.circ
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43a0	20 44 2e 20 42 2e 20 4a 6f 68 6e 73 6f 6e 2c 20 53 49 41 4d 20 4a 6f 75 72 6e 61 6c 20 6f 6e 20	.D..B..Johnson,.SIAM.Journal.on.
43c0	43 6f 6d 70 75 74 69 6e 67 20 34 2c 20 6e 6f 2e 20 31 2c 20 37 37 2d 38 34 2c 20 31 39 37 35 2e	Computing.4,.no..1,.77-84,.1975.
43e0	0a 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 64 6f 69 2e 6f 72 67 2f 31 30 2e 31 31 33 37 2f	........https://doi.org/10.1137/
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4460	61 74 68 da 07 62 6c 6f 63 6b 65 64 da 01 42 da 05 73 74 61 72 74 72 1e 00 00 00 da 06 63 6c 6f	ath..blocked..B..startr......clo
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44e0	0e 11 90 24 8b 69 80 47 dc 08 13 94 43 d3 08 18 80 41 d8 0c 10 90 11 89 47 80 45 dc 0d 11 90 21	...$.i.G....C....A......G.E....!
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45a0	88 41 d8 0f 15 8f 7a 89 7a 8c 7c d9 13 19 d8 21 25 90 46 98 32 91 4a d8 21 22 a0 03 90 0d d9 16	.A....z.z.|....!%.F.2.J.!"......
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4c40	2f 61 72 78 69 76 2e 6f 72 67 2f 61 62 73 2f 32 31 30 35 2e 31 30 30 39 34 0a 0a 20 20 20 20 72	/arxiv.org/abs/2105.10094......r
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4cc0	03 72 30 00 00 00 72 88 00 00 00 da 02 62 6c 73 03 00 00 00 20 20 80 72 28 00 00 00 72 33 00 00	.r0...r......bls.......r(...r3..
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4de0	20 20 20 20 20 20 20 20 20 40 72 28 00 00 00 72 63 00 00 00 72 63 00 00 00 a0 01 00 00 73 b6 01	.........@r(...rc...rc.......s..
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4e60	11 15 f2 00 19 09 20 88 41 d8 0f 10 90 45 8a 7a d8 16 1a 99 31 90 67 92 0d d8 1b 1c 90 04 90 52	........A....E.z....1.g........R
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4ec0	97 0c 91 0c 9c 54 a0 21 a0 41 a1 24 9b 5a d4 10 28 d9 10 15 f0 13 19 09 20 f0 16 00 0d 12 8f 49	.....T.!.A.$.Z..(..............I
4ee0	89 49 8c 4b d8 10 14 97 08 91 08 93 0a 88 41 d8 11 15 97 18 91 18 93 1a 88 42 d9 0f 13 dc 1b 1e	.I.K..........A..........B......
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4fa0	15 90 61 91 44 97 48 91 48 98 51 95 4b f0 03 01 11 20 f5 35 00 0b 10 f9 73 19 00 00 00 83 42 08	..a.D.H.H.Q.K......5....s.....B.
4fc0	46 39 01 c2 0c 44 07 46 39 01 c6 14 21 46 39 01 c6 37 02 46 39 01 63 02 00 00 00 00 00 00 00 00	F9...D.F9...!F9..7.F9.c.........
4fe0	00 00 00 09 00 00 00 23 00 00 00 f3 34 07 00 00 87 00 87 16 87 17 87 18 4b 00 01 00 97 00 7c 01	.......#....4...........K.....|.
5000	81 16 7c 01 64 02 6b 28 00 00 72 01 79 01 7c 01 64 02 6b 02 00 00 72 0b 74 01 00 00 00 00 00 00	..|.d.k(..r.y.|.d.k...r.t.......
5020	00 00 64 03 ab 01 00 00 00 00 00 00 82 01 89 00 6a 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00	..d.............j...............
5040	00 00 00 00 ab 00 00 00 00 00 00 00 7d 02 89 00 6a 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00	............}...j...............
5060	00 00 00 00 ab 00 00 00 00 00 00 00 7d 03 7c 03 72 2a 64 04 84 00 89 00 6a 06 00 00 00 00 00 00	............}.|.r*d.....j.......
5080	00 00 00 00 00 00 00 00 00 00 00 00 6a 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	............j...................
50a0	ab 00 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 45 00 64 01 7b 03 00 00 96 02 97 02 86 05	........D.........E.d.{.........
50c0	05 00 01 00 6e 29 64 05 84 00 89 00 6a 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	....n)d.....j...................
50e0	6a 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 44 00 ab 00	j...........................D...
5100	00 00 00 00 00 00 45 00 64 01 7b 03 00 00 96 02 97 02 86 05 05 00 01 00 7c 01 81 06 7c 01 64 06	......E.d.{.............|...|.d.
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51a0	ab 01 00 00 00 00 00 00 8a 16 89 16 6a 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	............j...................
51c0	64 08 ac 09 ab 01 00 00 00 00 00 00 7d 05 6e 17 74 0d 00 00 00 00 00 00 00 00 6a 14 00 00 00 00	d...........}.n.t.........j.....
51e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 04 ab 01 00 00 00 00 00 00 8a 16 64 01 7d 05 7c 03	..............|...........d.}.|.
5200	72 db 7c 02 73 1a 89 16 6a 17 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00	r.|.s...j.......................
5220	00 00 00 00 7d 05 74 0b 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 8a 18 89 00 6a 06 00 00	....}.t.....................j...
5240	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00	................j...............
5260	00 00 00 00 ab 00 00 00 00 00 00 00 44 00 5d a2 00 00 5c 02 00 00 7d 06 7d 07 7c 06 89 17 76 00	............D.]...\...}.}.|...v.
5280	72 01 8c 0b 7c 02 72 3f 64 0a 84 00 7c 07 6a 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	r...|.r?d...|.j.................
52a0	00 00 ab 00 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 7d 08 7c 08 44 00 5d 22 00 00 5c 02	..........D.........}.|.D.]"..\.
52c0	00 00 7d 09 7d 0a 7c 0a 64 06 6b 44 00 00 73 01 8c 0c 89 16 6a 19 00 00 00 00 00 00 00 00 00 00	..}.}.|.d.kD..s.....j...........
52e0	00 00 00 00 00 00 00 00 7c 06 7c 09 66 02 7c 09 7c 06 66 02 66 02 ab 01 00 00 00 00 00 00 01 00	........|.|.f.|.|.f.f...........
5300	8c 24 04 00 8c 4c 88 18 66 01 64 0b 84 08 7c 07 6a 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00	.$...L..f.d...|.j...............
5320	00 00 00 00 ab 00 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 7d 08 7c 08 44 00 5d 28 00 00	............D.........}.|.D.](..
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5380	7c 06 7c 09 ab 02 00 00 00 00 00 00 01 00 8c 2a 04 00 89 18 6a 1d 00 00 00 00 00 00 00 00 00 00	|.|............*....j...........
53a0	00 00 00 00 00 00 00 00 7c 06 ab 01 00 00 00 00 00 00 01 00 8c a4 04 00 7c 02 72 79 89 16 6a 06	........|...............|.ry..j.
53c0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 09 00 00 00 00 00 00 00 00 00 00 00 00	..................j.............
53e0	00 00 00 00 00 00 ab 00 00 00 00 00 00 00 44 00 5d 5c 00 00 5c 02 00 00 7d 06 7d 0b 7c 0b 44 00	..............D.]\..\...}.}.|.D.
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5420	00 00 00 00 7c 09 7c 06 ab 02 00 00 00 00 00 00 73 01 8c 16 7c 06 7c 09 67 02 91 02 8c 1b 04 00	....|.|.........s...|.|.g.......
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54a0	ab 01 00 00 00 00 00 00 01 00 8c 5e 04 00 7c 01 81 06 7c 01 64 0c 6b 28 00 00 72 01 79 01 7c 02	...........^..|...|.d.k(..r.y.|.
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5500	00 00 00 00 00 00 00 00 00 00 00 00 00 00 7d 0d 88 16 66 01 64 0f 84 08 7d 0e 02 00 7c 0d 89 16	..............}...f.d...}...|...
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55a0	00 00 00 00 ab 01 00 00 00 00 00 00 7d 09 89 16 6a 2d 00 00 00 00 00 00 00 00 00 00 00 00 00 00	............}...j-..............
55c0	00 00 00 00 7c 0f ab 01 00 00 00 00 00 00 7d 11 64 01 78 01 7d 12 7d 13 02 00 7c 0e 7c 11 7c 09	....|.........}.d.x.}.}...|.|.|.
55e0	ab 02 00 00 00 00 00 00 44 00 5d 4d 00 00 5c 02 00 00 7d 14 7d 15 7c 15 72 05 7c 14 96 01 97 01	........D.]M..\...}.}.|.r.|.....
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5620	80 02 7c 12 6e 19 74 2f 00 00 00 00 00 00 00 00 7c 05 6a 2d 00 00 00 00 00 00 00 00 00 00 00 00	..|.n.t/........|.j-............
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5660	00 00 00 00 7c 12 7c 13 7c 14 7c 01 ab 04 00 00 00 00 00 00 45 00 64 01 7b 03 00 00 96 02 97 02	....|.|.|.|.........E.d.{.......
5680	86 05 05 00 01 00 8c 4f 04 00 7c 10 6a 33 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	.......O..|.j3..................
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57c0	61 64 64 69 74 69 6f 6e 61 6c 20 65 64 67 65 20 62 65 74 77 65 65 6e 20 74 77 6f 20 6e 6f 64 65	additional.edge.between.two.node
57e0	73 20 69 6e 20 74 68 65 20 63 79 63 6c 65 2e 20 20 41 0a 20 20 20 20 60 63 68 6f 72 64 6c 65 73	s.in.the.cycle...A.....`chordles
5800	73 20 63 79 63 6c 65 60 20 69 73 20 61 20 73 69 6d 70 6c 65 20 63 79 63 6c 65 20 77 69 74 68 6f	s.cycle`.is.a.simple.cycle.witho
5820	75 74 20 63 68 6f 72 64 73 2e 20 20 53 61 69 64 20 64 69 66 66 65 72 65 6e 74 6c 79 2c 20 61 0a	ut.chords...Said.differently,.a.
5840	20 20 20 20 63 68 6f 72 64 6c 65 73 73 20 63 79 63 6c 65 20 69 73 20 61 20 63 79 63 6c 65 20 43	....chordless.cycle.is.a.cycle.C
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58a0	20 47 5b 43 5d 20 69 73 20 65 71 75 61 6c 20 74 6f 20 74 68 65 20 6c 65 6e 67 74 68 20 6f 66 20	.G[C].is.equal.to.the.length.of.
58c0	60 43 60 2e 0a 0a 20 20 20 20 4e 6f 74 65 20 74 68 61 74 20 73 6f 6d 65 20 63 61 72 65 20 6d 75	`C`.......Note.that.some.care.mu
58e0	73 74 20 62 65 20 74 61 6b 65 6e 20 69 6e 20 74 68 65 20 63 61 73 65 20 74 68 61 74 20 47 20 69	st.be.taken.in.the.case.that.G.i
5900	73 20 6e 6f 74 20 61 20 73 69 6d 70 6c 65 20 67 72 61 70 68 0a 20 20 20 20 6e 6f 72 20 61 20 73	s.not.a.simple.graph.....nor.a.s
5920	69 6d 70 6c 65 20 64 69 67 72 61 70 68 2e 20 20 53 6f 6d 65 20 61 75 74 68 6f 72 73 20 6c 69 6d	imple.digraph...Some.authors.lim
5940	69 74 20 74 68 65 20 64 65 66 69 6e 69 74 69 6f 6e 20 6f 66 20 63 68 6f 72 64 6c 65 73 73 20 63	it.the.definition.of.chordless.c
5960	79 63 6c 65 73 0a 20 20 20 20 74 6f 20 68 61 76 65 20 61 20 70 72 65 73 63 72 69 62 65 64 20 6d	ycles.....to.have.a.prescribed.m
5980	69 6e 69 6d 75 6d 20 6c 65 6e 67 74 68 3b 20 77 65 20 64 6f 20 6e 6f 74 2e 0a 0a 20 20 20 20 20	inimum.length;.we.do.not........
59a0	20 20 20 31 2e 20 57 65 20 69 6e 74 65 72 70 72 65 74 20 73 65 6c 66 2d 6c 6f 6f 70 73 20 74 6f	...1..We.interpret.self-loops.to
59c0	20 62 65 20 63 68 6f 72 64 6c 65 73 73 20 63 79 63 6c 65 73 2c 20 65 78 63 65 70 74 20 69 6e 20	.be.chordless.cycles,.except.in.
59e0	6d 75 6c 74 69 67 72 61 70 68 73 0a 20 20 20 20 20 20 20 20 20 20 20 77 69 74 68 20 6d 75 6c 74	multigraphs............with.mult
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5a20	65 2c 20 69 6e 20 61 20 63 68 6f 72 64 6c 65 73 73 20 63 79 63 6c 65 20 6f 66 0a 20 20 20 20 20	e,.in.a.chordless.cycle.of......
5a40	20 20 20 20 20 20 6c 65 6e 67 74 68 20 67 72 65 61 74 65 72 20 74 68 61 6e 20 31 2c 20 74 68 65	......length.greater.than.1,.the
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5a80	70 73 2e 0a 0a 20 20 20 20 20 20 20 20 32 2e 20 57 65 20 69 6e 74 65 72 70 72 65 74 20 64 69 72	ps...........2..We.interpret.dir
5aa0	65 63 74 65 64 20 74 77 6f 2d 63 79 63 6c 65 73 20 74 6f 20 62 65 20 63 68 6f 72 64 6c 65 73 73	ected.two-cycles.to.be.chordless
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5ae0	6c 74 69 2d 64 69 67 72 61 70 68 73 20 77 68 65 6e 20 61 6e 79 20 65 64 67 65 20 69 6e 20 61 20	lti-digraphs.when.any.edge.in.a.
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5b20	20 20 20 20 20 20 20 20 33 2e 20 57 65 20 69 6e 74 65 72 70 72 65 74 20 70 61 72 61 6c 6c 65 6c	........3..We.interpret.parallel
5b40	20 70 61 69 72 73 20 6f 66 20 75 6e 64 69 72 65 63 74 65 64 20 65 64 67 65 73 20 61 73 20 74 77	.pairs.of.undirected.edges.as.tw
5b60	6f 2d 63 79 63 6c 65 73 2c 20 65 78 63 65 70 74 0a 20 20 20 20 20 20 20 20 20 20 20 77 68 65 6e	o-cycles,.except............when
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5bc0	20 20 20 20 20 20 20 20 34 2e 20 47 65 6e 65 72 61 6c 69 7a 69 6e 67 20 74 68 65 20 61 62 6f 76	........4..Generalizing.the.abov
5be0	65 2c 20 65 64 67 65 73 20 77 69 74 68 20 70 61 72 61 6c 6c 65 6c 20 63 6c 6f 6e 65 73 20 6d 61	e,.edges.with.parallel.clones.ma
5c00	79 20 6e 6f 74 20 6f 63 63 75 72 20 69 6e 0a 20 20 20 20 20 20 20 20 20 20 20 63 68 6f 72 64 6c	y.not.occur.in............chordl
5c20	65 73 73 20 63 79 63 6c 65 73 2e 0a 0a 20 20 20 20 49 6e 20 61 20 64 69 72 65 63 74 65 64 20 67	ess.cycles.......In.a.directed.g
5c40	72 61 70 68 2c 20 74 77 6f 20 63 68 6f 72 64 6c 65 73 73 20 63 79 63 6c 65 73 20 61 72 65 20 64	raph,.two.chordless.cycles.are.d
5c60	69 73 74 69 6e 63 74 20 69 66 20 74 68 65 79 20 61 72 65 20 6e 6f 74 0a 20 20 20 20 63 79 63 6c	istinct.if.they.are.not.....cycl
5c80	69 63 20 70 65 72 6d 75 74 61 74 69 6f 6e 73 20 6f 66 20 65 61 63 68 20 6f 74 68 65 72 2e 20 20	ic.permutations.of.each.other...
5ca0	49 6e 20 61 6e 20 75 6e 64 69 72 65 63 74 65 64 20 67 72 61 70 68 2c 20 74 77 6f 20 63 68 6f 72	In.an.undirected.graph,.two.chor
5cc0	64 6c 65 73 73 0a 20 20 20 20 63 79 63 6c 65 73 20 61 72 65 20 64 69 73 74 69 6e 63 74 20 69 66	dless.....cycles.are.distinct.if
5ce0	20 74 68 65 79 20 61 72 65 20 6e 6f 74 20 63 79 63 6c 69 63 20 70 65 72 6d 75 74 61 74 69 6f 6e	.they.are.not.cyclic.permutation
5d00	73 20 6f 66 20 65 61 63 68 20 6f 74 68 65 72 20 6e 6f 72 20 6f 66 0a 20 20 20 20 74 68 65 20 6f	s.of.each.other.nor.of.....the.o
5d20	74 68 65 72 27 73 20 72 65 76 65 72 73 61 6c 2e 0a 0a 20 20 20 20 4f 70 74 69 6f 6e 61 6c 6c 79	ther's.reversal.......Optionally
5d40	2c 20 74 68 65 20 63 79 63 6c 65 73 20 61 72 65 20 62 6f 75 6e 64 65 64 20 69 6e 20 6c 65 6e 67	,.the.cycles.are.bounded.in.leng
5d60	74 68 2e 0a 0a 20 20 20 20 57 65 20 75 73 65 20 61 6e 20 61 6c 67 6f 72 69 74 68 6d 20 73 74 72	th.......We.use.an.algorithm.str
5d80	6f 6e 67 6c 79 20 69 6e 73 70 69 72 65 64 20 62 79 20 74 68 61 74 20 6f 66 20 44 69 61 73 20 65	ongly.inspired.by.that.of.Dias.e
5da0	74 20 61 6c 20 5b 31 5d 5f 2e 20 20 49 74 20 68 61 73 0a 20 20 20 20 62 65 65 6e 20 6d 6f 64 69	t.al.[1]_...It.has.....been.modi
5dc0	66 69 65 64 20 69 6e 20 74 68 65 20 66 6f 6c 6c 6f 77 69 6e 67 20 77 61 79 73 3a 0a 0a 20 20 20	fied.in.the.following.ways:.....
5de0	20 20 20 20 20 31 2e 20 52 65 63 75 72 73 69 6f 6e 20 69 73 20 61 76 6f 69 64 65 64 2c 20 70 65	.....1..Recursion.is.avoided,.pe
5e00	72 20 50 79 74 68 6f 6e 27 73 20 6c 69 6d 69 74 61 74 69 6f 6e 73 0a 0a 20 20 20 20 20 20 20 20	r.Python's.limitations..........
5e20	32 2e 20 54 68 65 20 6c 61 62 65 6c 69 6e 67 20 66 75 6e 63 74 69 6f 6e 20 69 73 20 6e 6f 74 20	2..The.labeling.function.is.not.
5e40	6e 65 63 65 73 73 61 72 79 2c 20 62 65 63 61 75 73 65 20 74 68 65 20 73 74 61 72 74 69 6e 67 20	necessary,.because.the.starting.
5e60	70 61 74 68 73 0a 20 20 20 20 20 20 20 20 20 20 20 20 61 72 65 20 63 68 6f 73 65 6e 20 28 61 6e	paths.............are.chosen.(an
5e80	64 20 64 65 6c 65 74 65 64 20 66 72 6f 6d 20 74 68 65 20 68 6f 73 74 20 67 72 61 70 68 29 20 74	d.deleted.from.the.host.graph).t
5ea0	6f 20 70 72 65 76 65 6e 74 20 6d 75 6c 74 69 70 6c 65 0a 20 20 20 20 20 20 20 20 20 20 20 20 6f	o.prevent.multiple.............o
5ec0	63 63 75 72 72 65 6e 63 65 73 20 6f 66 20 74 68 65 20 73 61 6d 65 20 70 61 74 68 0a 0a 20 20 20	ccurrences.of.the.same.path.....
5ee0	20 20 20 20 20 33 2e 20 54 68 65 20 73 65 61 72 63 68 20 69 73 20 6f 70 74 69 6f 6e 61 6c 6c 79	.....3..The.search.is.optionally
5f00	20 62 6f 75 6e 64 65 64 20 61 74 20 61 20 73 70 65 63 69 66 69 65 64 20 6c 65 6e 67 74 68 0a 0a	.bounded.at.a.specified.length..
5f20	20 20 20 20 20 20 20 20 34 2e 20 53 75 70 70 6f 72 74 20 66 6f 72 20 64 69 72 65 63 74 65 64 20	........4..Support.for.directed.
5f40	67 72 61 70 68 73 20 69 73 20 70 72 6f 76 69 64 65 64 20 62 79 20 65 78 74 65 6e 64 69 6e 67 20	graphs.is.provided.by.extending.
5f60	63 79 63 6c 65 73 20 61 6c 6f 6e 67 0a 20 20 20 20 20 20 20 20 20 20 20 20 66 6f 72 77 61 72 64	cycles.along.............forward
5f80	20 65 64 67 65 73 2c 20 61 6e 64 20 62 6c 6f 63 6b 69 6e 67 20 6e 6f 64 65 73 20 61 6c 6f 6e 67	.edges,.and.blocking.nodes.along
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5fc0	20 20 20 20 35 2e 20 53 75 70 70 6f 72 74 20 66 6f 72 20 6d 75 6c 74 69 67 72 61 70 68 73 20 69	....5..Support.for.multigraphs.i
5fe0	73 20 70 72 6f 76 69 64 65 64 20 62 79 20 6f 6d 69 74 74 69 6e 67 20 64 69 67 6f 6e 73 20 66 72	s.provided.by.omitting.digons.fr
6000	6f 6d 20 74 68 65 20 73 65 74 0a 20 20 20 20 20 20 20 20 20 20 20 20 6f 66 20 66 6f 72 77 61 72	om.the.set.............of.forwar
6020	64 20 65 64 67 65 73 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d	d.edges......Parameters.....----
6040	2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 20 3a 20 4e 65 74 77 6f 72 6b 58 20 44 69 47 72 61 70 68 0a	------.....G.:.NetworkX.DiGraph.
6060	20 20 20 20 20 20 20 41 20 64 69 72 65 63 74 65 64 20 67 72 61 70 68 0a 0a 20 20 20 20 6c 65 6e	.......A.directed.graph......len
6080	67 74 68 5f 62 6f 75 6e 64 20 3a 20 69 6e 74 20 6f 72 20 4e 6f 6e 65 2c 20 6f 70 74 69 6f 6e 61	gth_bound.:.int.or.None,.optiona
60a0	6c 20 28 64 65 66 61 75 6c 74 3d 4e 6f 6e 65 29 0a 20 20 20 20 20 20 20 49 66 20 6c 65 6e 67 74	l.(default=None)........If.lengt
60c0	68 5f 62 6f 75 6e 64 20 69 73 20 61 6e 20 69 6e 74 2c 20 67 65 6e 65 72 61 74 65 20 61 6c 6c 20	h_bound.is.an.int,.generate.all.
60e0	73 69 6d 70 6c 65 20 63 79 63 6c 65 73 20 6f 66 20 47 20 77 69 74 68 20 6c 65 6e 67 74 68 20 61	simple.cycles.of.G.with.length.a
6100	74 0a 20 20 20 20 20 20 20 6d 6f 73 74 20 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 2e 20 20 4f 74 68	t........most.length_bound...Oth
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6140	65 73 20 6f 66 20 47 2e 0a 0a 20 20 20 20 59 69 65 6c 64 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 0a	es.of.G.......Yields.....------.
6160	20 20 20 20 6c 69 73 74 20 6f 66 20 6e 6f 64 65 73 0a 20 20 20 20 20 20 20 45 61 63 68 20 63 79	....list.of.nodes........Each.cy
6180	63 6c 65 20 69 73 20 72 65 70 72 65 73 65 6e 74 65 64 20 62 79 20 61 20 6c 69 73 74 20 6f 66 20	cle.is.represented.by.a.list.of.
61a0	6e 6f 64 65 73 20 61 6c 6f 6e 67 20 74 68 65 20 63 79 63 6c 65 2e 0a 0a 20 20 20 20 45 78 61 6d	nodes.along.the.cycle.......Exam
61c0	70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 73 6f 72 74 65 64	ples.....--------.....>>>.sorted
61e0	28 6c 69 73 74 28 6e 78 2e 63 68 6f 72 64 6c 65 73 73 5f 63 79 63 6c 65 73 28 6e 78 2e 63 6f 6d	(list(nx.chordless_cycles(nx.com
6200	70 6c 65 74 65 5f 67 72 61 70 68 28 34 29 29 29 29 0a 20 20 20 20 5b 5b 31 2c 20 30 2c 20 32 5d	plete_graph(4)))).....[[1,.0,.2]
6220	2c 20 5b 31 2c 20 30 2c 20 33 5d 2c 20 5b 32 2c 20 30 2c 20 33 5d 2c 20 5b 32 2c 20 31 2c 20 33	,.[1,.0,.3],.[2,.0,.3],.[2,.1,.3
6240	5d 5d 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 57 68 65 6e	]]......Notes.....-----.....When
6260	20 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 20 69 73 20 4e 6f 6e 65 2c 20 61 6e 64 20 74 68 65 20 67	.length_bound.is.None,.and.the.g
6280	72 61 70 68 20 69 73 20 73 69 6d 70 6c 65 2c 20 74 68 65 20 74 69 6d 65 20 63 6f 6d 70 6c 65 78	raph.is.simple,.the.time.complex
62a0	69 74 79 20 69 73 0a 20 20 20 20 24 4f 28 28 6e 2b 65 29 28 63 2b 31 29 29 24 20 66 6f 72 20 24	ity.is.....$O((n+e)(c+1))$.for.$
62c0	6e 24 20 6e 6f 64 65 73 2c 20 24 65 24 20 65 64 67 65 73 20 61 6e 64 20 24 63 24 20 63 68 6f 72	n$.nodes,.$e$.edges.and.$c$.chor
62e0	64 6c 65 73 73 20 63 79 63 6c 65 73 2e 0a 0a 20 20 20 20 52 61 69 73 65 73 0a 20 20 20 20 2d 2d	dless.cycles.......Raises.....--
6300	2d 2d 2d 2d 0a 20 20 20 20 56 61 6c 75 65 45 72 72 6f 72 0a 20 20 20 20 20 20 20 20 77 68 65 6e	----.....ValueError.........when
6320	20 6c 65 6e 67 74 68 5f 62 6f 75 6e 64 20 3c 20 30 2e 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63	.length_bound.<.0.......Referenc
6340	65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 45 66 66	es.....----------........[1].Eff
6360	69 63 69 65 6e 74 20 65 6e 75 6d 65 72 61 74 69 6f 6e 20 6f 66 20 63 68 6f 72 64 6c 65 73 73 20	icient.enumeration.of.chordless.
6380	63 79 63 6c 65 73 0a 20 20 20 20 20 20 20 45 2e 20 44 69 61 73 20 61 6e 64 20 44 2e 20 43 61 73	cycles........E..Dias.and.D..Cas
63a0	74 6f 6e 67 75 61 79 20 61 6e 64 20 48 2e 20 4c 6f 6e 67 6f 20 61 6e 64 20 57 2e 41 2e 52 2e 20	tonguay.and.H..Longo.and.W.A.R..
63c0	4a 72 61 64 69 0a 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 61 72 78 69 76 2e 6f 72 67 2f 61	Jradi........https://arxiv.org/a
63e0	62 73 2f 31 33 30 39 2e 31 30 35 31 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d	bs/1309.1051......See.Also.....-
6400	2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 0a 20 20 20 20 4e 72	-------.....simple_cycles.....Nr
6420	02 00 00 00 72 2b 00 00 00 63 01 00 00 00 00 00 00 00 00 00 00 00 07 00 00 00 33 00 00 00 f3 66	....r+...c................3....f
6440	00 00 00 4b 00 01 00 97 00 7c 00 5d 29 00 00 5c 02 00 00 7d 01 7d 02 74 01 00 00 00 00 00 00 00	...K.....|.])..\...}.}.t........
6460	00 7c 02 6a 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 01 64 00 ab 02 00 00 00	.|.j...................|.d......
6480	00 00 00 ab 01 00 00 00 00 00 00 64 01 6b 28 00 00 73 01 8c 25 7c 01 67 01 96 01 97 01 01 00 8c	...........d.k(..s..%|.g........
64a0	2b 04 00 79 02 ad 03 77 01 29 03 72 2e 00 00 00 72 35 00 00 00 4e 29 02 72 38 00 00 00 72 8d 00	+..y...w.).r....r5...N).r8...r..
64c0	00 00 72 2f 00 00 00 73 03 00 00 00 20 20 20 72 28 00 00 00 72 33 00 00 00 7a 23 63 68 6f 72 64	..r/...s.......r(...r3...z#chord
64e0	6c 65 73 73 5f 63 79 63 6c 65 73 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 3e 42 02	less_cycles.<locals>.<genexpr>B.
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6560	7c 00 5d 0f 00 00 5c 02 00 00 7d 01 7d 02 7c 01 7c 02 76 00 73 01 8c 0b 7c 01 67 01 96 01 97 01	|.]...\...}.}.|.|.v.s...|.g.....
6580	01 00 8c 11 04 00 79 00 ad 03 77 01 72 2d 00 00 00 72 2e 00 00 00 72 2f 00 00 00 73 03 00 00 00	......y...w.r-...r....r/...s....
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6600	00 63 01 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 33 00 00 00 f3 62 00 00 00 95 02 4b 00 01	.c................3....b.....K..
6620	00 97 00 7c 00 5d 26 00 00 7d 01 7c 01 89 04 76 01 73 01 8c 08 89 03 6a 00 00 00 00 00 00 00 00	...|.]&..}.|...v.s.....j........
6640	00 00 00 00 00 00 00 00 00 00 00 7c 01 19 00 00 00 44 00 5d 0d 00 00 7d 02 7c 02 89 04 76 01 73	...........|.....D.]...}.|...v.s
6660	01 8c 08 7c 01 7c 02 66 02 96 01 97 01 01 00 8c 0f 04 00 8c 28 04 00 79 00 ad 03 77 01 72 2d 00	...|.|.f............(..y...w.r-.
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6740	00 00 00 00 00 00 00 00 00 05 00 00 00 33 00 00 00 f3 3c 00 00 00 4b 00 01 00 97 00 7c 00 5d 14	.............3....<...K.....|.].
6760	00 00 5c 02 00 00 7d 01 7d 02 7c 01 74 01 00 00 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00	..\...}.}.|.t.........|.........
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67c0	23 63 68 6f 72 64 6c 65 73 73 5f 63 79 63 6c 65 73 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65	#chordless_cycles.<locals>.<gene
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78c0	69 6e 67 20 64 69 67 6f 6e 73 20 66 72 6f 6d 20 74 68 65 20 73 65 74 0a 20 20 20 20 20 20 20 20	ing.digons.from.the.set.........
78e0	20 20 20 20 6f 66 20 66 6f 72 77 61 72 64 20 65 64 67 65 73 0a 0a 20 20 20 20 50 61 72 61 6d 65	....of.forward.edges......Parame
7900	74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 46 20 3a 20 5f 4e 65 69	ters.....----------.....F.:._Nei
7920	67 68 62 6f 72 68 6f 6f 64 43 61 63 68 65 0a 20 20 20 20 20 20 20 41 20 67 72 61 70 68 20 6f 66	ghborhoodCache........A.graph.of
7940	20 66 6f 72 77 61 72 64 20 65 64 67 65 73 20 74 6f 20 66 6f 6c 6c 6f 77 20 69 6e 20 63 6f 6e 73	.forward.edges.to.follow.in.cons
7960	74 72 75 63 74 69 6e 67 20 63 79 63 6c 65 73 0a 0a 20 20 20 20 42 20 3a 20 5f 4e 65 69 67 68 62	tructing.cycles......B.:._Neighb
7980	6f 72 68 6f 6f 64 43 61 63 68 65 0a 20 20 20 20 20 20 20 41 20 67 72 61 70 68 20 6f 66 20 62 6c	orhoodCache........A.graph.of.bl
79a0	6f 63 6b 69 6e 67 20 65 64 67 65 73 20 74 6f 20 70 72 65 76 65 6e 74 20 74 68 65 20 70 72 6f 64	ocking.edges.to.prevent.the.prod
79c0	75 63 74 69 6f 6e 20 6f 66 20 63 68 6f 72 64 6c 65 73 73 20 63 79 63 6c 65 73 0a 0a 20 20 20 20	uction.of.chordless.cycles......
79e0	70 61 74 68 20 3a 20 6c 69 73 74 0a 20 20 20 20 20 20 20 41 20 63 79 63 6c 65 20 70 72 65 66 69	path.:.list........A.cycle.prefi
7a00	78 2e 20 20 41 6c 6c 20 63 79 63 6c 65 73 20 67 65 6e 65 72 61 74 65 64 20 77 69 6c 6c 20 62 65	x...All.cycles.generated.will.be
7a20	67 69 6e 20 77 69 74 68 20 74 68 69 73 20 70 72 65 66 69 78 2e 0a 0a 20 20 20 20 6c 65 6e 67 74	gin.with.this.prefix.......lengt
7a40	68 5f 62 6f 75 6e 64 20 3a 20 69 6e 74 0a 20 20 20 20 20 20 20 41 20 6c 65 6e 67 74 68 20 62 6f	h_bound.:.int........A.length.bo
7a60	75 6e 64 2e 20 20 41 6c 6c 20 63 79 63 6c 65 73 20 67 65 6e 65 72 61 74 65 64 20 77 69 6c 6c 20	und...All.cycles.generated.will.
7a80	68 61 76 65 20 6c 65 6e 67 74 68 20 61 74 20 6d 6f 73 74 20 6c 65 6e 67 74 68 5f 62 6f 75 6e 64	have.length.at.most.length_bound
7aa0	2e 0a 0a 0a 20 20 20 20 59 69 65 6c 64 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6c 69	........Yields.....------.....li
7ac0	73 74 20 6f 66 20 6e 6f 64 65 73 0a 20 20 20 20 20 20 20 45 61 63 68 20 63 79 63 6c 65 20 69 73	st.of.nodes........Each.cycle.is
7ae0	20 72 65 70 72 65 73 65 6e 74 65 64 20 62 79 20 61 20 6c 69 73 74 20 6f 66 20 6e 6f 64 65 73 20	.represented.by.a.list.of.nodes.
7b00	61 6c 6f 6e 67 20 74 68 65 20 63 79 63 6c 65 2e 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73	along.the.cycle.......References
7b20	0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 45 66 66 69 63	.....----------........[1].Effic
7b40	69 65 6e 74 20 65 6e 75 6d 65 72 61 74 69 6f 6e 20 6f 66 20 63 68 6f 72 64 6c 65 73 73 20 63 79	ient.enumeration.of.chordless.cy
7b60	63 6c 65 73 0a 20 20 20 20 20 20 20 45 2e 20 44 69 61 73 20 61 6e 64 20 44 2e 20 43 61 73 74 6f	cles........E..Dias.and.D..Casto
7b80	6e 67 75 61 79 20 61 6e 64 20 48 2e 20 4c 6f 6e 67 6f 20 61 6e 64 20 57 2e 41 2e 52 2e 20 4a 72	nguay.and.H..Longo.and.W.A.R..Jr
7ba0	61 64 69 0a 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 61 72 78 69 76 2e 6f 72 67 2f 61 62 73	adi........https://arxiv.org/abs
7bc0	2f 31 33 30 39 2e 31 30 35 31 0a 0a 20 20 20 20 72 02 00 00 00 72 35 00 00 00 4e 72 46 00 00 00	/1309.1051......r....r5...NrF...
7be0	72 7e 00 00 00 29 06 72 03 00 00 00 da 03 69 6e 74 72 61 00 00 00 72 38 00 00 00 72 18 00 00 00	r~...).r......intra...r8...r....
7c00	72 17 00 00 00 29 0c 72 a2 00 00 00 72 84 00 00 00 72 82 00 00 00 72 55 00 00 00 72 83 00 00 00	r....).r....r....r....rU...r....
7c20	da 06 74 61 72 67 65 74 72 88 00 00 00 72 31 00 00 00 72 1e 00 00 00 72 87 00 00 00 da 02 46 77	..targetr....r1...r....r......Fw
7c40	da 02 42 77 73 0c 00 00 00 20 20 20 20 20 20 20 20 20 20 20 20 72 28 00 00 00 72 ab 00 00 00 72	..Bws................r(...r....r
7c60	ab 00 00 00 b4 02 00 00 73 4b 01 00 00 e8 00 f8 80 00 f4 5e 01 00 0f 1a 9c 23 d3 0e 1e 80 47 d8	........sK.........^.....#....G.
7c80	0d 11 90 21 89 57 80 46 d8 17 18 80 47 88 44 90 11 89 47 d1 04 14 d8 0d 11 90 21 90 22 88 58 f2	...!.W.F....G.D...G.......!.".X.
7ca0	00 02 05 1c 88 01 d8 11 12 90 31 91 14 f2 00 01 09 1c 88 41 d8 0c 13 90 41 8b 4a 98 21 89 4f 8c	..........1........A....A.J.!.O.
7cc0	4a f1 03 01 09 1c f0 03 02 05 1c f4 08 00 0e 12 90 21 90 44 98 11 91 47 91 2a d3 0d 1d d0 0c 1e	J................!.D...G.*......
7ce0	80 45 d9 0a 0f d8 0f 14 90 52 89 79 88 04 d8 11 15 f2 00 11 09 20 88 41 d8 0f 16 90 71 89 7a 98	.E.......R.y...........A....q.z.
7d00	51 8b 7f a0 4c d0 24 38 bc 43 c0 04 bb 49 c8 0c d3 3c 54 d8 15 16 90 71 91 54 90 02 d8 13 19 98	Q...L.$8.C...I...<T....q.T......
7d20	52 91 3c d8 1a 1e a0 21 a0 13 99 2a d3 14 24 e0 19 1a 98 31 99 14 90 42 d8 17 1d a0 12 91 7c d8	R.<....!...*..$....1...B......|.
7d40	18 20 d8 1d 1f f2 00 01 15 28 98 01 d8 18 1f a0 01 9b 0a a0 61 99 0f 9c 0a f0 03 01 15 28 e0 14	.........(..........a........(..
7d60	18 97 4b 91 4b a0 01 94 4e d8 14 19 97 4c 91 4c a4 14 a0 62 a3 18 d4 14 2a d9 14 19 f0 1b 11 09	..K.K...N....L.L...b....*.......
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7da0	d8 10 17 98 01 93 0a 98 61 91 0f 94 0a f0 03 01 0d 20 f4 25 00 0b 10 f9 73 19 00 00 00 82 41 24	........a..........%....s.....A$
7dc0	44 10 01 c1 27 10 44 10 01 c1 38 42 15 44 10 01 c4 0e 02 44 10 01 da 0a 75 6e 64 69 72 65 63 74	D...'.D...8B.D.....D....undirect
7de0	65 64 54 29 01 da 0d 6d 75 74 61 74 65 73 5f 69 6e 70 75 74 63 01 00 00 00 00 00 00 00 00 00 00	edT)...mutates_inputc...........
7e00	00 0a 00 00 00 03 00 00 00 f3 7e 02 00 00 87 09 87 0a 87 0b 87 0c 87 0d 87 0e 87 0f 87 10 97 00	..........~.....................
7e20	88 09 88 0a 88 0b 66 03 64 01 84 08 8a 0a 88 09 88 0a 88 0b 88 0c 88 0e 88 0f 66 06 64 02 84 08	......f.d.................f.d...
7e40	8a 0c 67 00 8a 0e 74 01 00 00 00 00 00 00 00 00 74 02 00 00 00 00 00 00 00 00 ab 01 00 00 00 00	..g...t.........t...............
7e60	00 00 8a 0b 74 01 00 00 00 00 00 00 00 00 74 04 00 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00	....t.........t.................
7e80	8a 09 67 00 8a 0f 7c 00 44 00 5d 39 00 00 7d 01 7c 00 6a 07 00 00 00 00 00 00 00 00 00 00 00 00	..g...|.D.]9..}.|.j.............
7ea0	00 00 00 00 00 00 7c 01 7c 01 ab 02 00 00 00 00 00 00 73 01 8c 16 89 0f 6a 09 00 00 00 00 00 00	......|.|.........s.....j.......
7ec0	00 00 00 00 00 00 00 00 00 00 00 00 7c 01 67 01 ab 01 00 00 00 00 00 00 01 00 7c 00 6a 0b 00 00	............|.g...........|.j...
7ee0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 01 7c 01 ab 02 00 00 00 00 00 00 01 00 8c 3b	................|.|............;
7f00	04 00 74 0d 00 00 00 00 00 00 00 00 74 0f 00 00 00 00 00 00 00 00 7c 00 74 11 00 00 00 00 00 00	..t.........t.........|.t.......
7f20	00 00 74 13 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 ab 02	..t.........|...................
7f40	00 00 00 00 00 00 ab 01 00 00 00 00 00 00 8a 0d 89 0d 44 00 5d 97 00 00 8a 10 7c 00 6a 15 00 00	..................D.].....|.j...
7f60	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 88 0d 88 10 66 02 64 03 84 08 7c 00 44 00 ab 00	....................f.d...|.D...
7f80	00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7d 02 74 17 00 00 00 00 00 00 00 00 6a 18 00 00 00 00	..............}.t.........j.....
7fa0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 7d 03 74 1b 00 00 00 00	..............|.........}.t.....
7fc0	00 00 00 00 7c 03 88 0d 66 01 64 04 84 08 ac 05 ab 02 00 00 00 00 00 00 7d 04 7c 00 6a 15 00 00	....|...f.d.............}.|.j...
7fe0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 04 ab 01 00 00 00 00 00 00 7d 05 74 13 00 00	................|.........}.t...
8000	00 00 00 00 00 00 7c 05 ab 01 00 00 00 00 00 00 64 06 6b 44 00 00 73 01 8c 63 74 1b 00 00 00 00	......|.........d.kD..s..ct.....
8020	00 00 00 00 7c 05 89 0d 6a 1c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ac 05 ab 02	....|...j.......................
8040	00 00 00 00 00 00 7d 06 7c 05 44 00 5d 0f 00 00 7d 07 64 07 89 0b 7c 07 3c 00 00 00 67 00 89 09	......}.|.D.]...}.d...|.<...g...
8060	7c 07 19 00 00 00 64 08 64 08 1b 00 8c 11 04 00 02 00 89 0c 7c 06 7c 06 7c 05 ab 03 00 00 00 00	|.....d.d...........|.|.|.......
8080	00 00 7d 08 8c 99 04 00 89 0f 53 00 29 09 61 3e 05 00 00 46 69 6e 64 20 73 69 6d 70 6c 65 20 63	..}.......S.).a>...Find.simple.c
80a0	79 63 6c 65 73 20 28 65 6c 65 6d 65 6e 74 61 72 79 20 63 69 72 63 75 69 74 73 29 20 6f 66 20 61	ycles.(elementary.circuits).of.a
80c0	20 64 69 72 65 63 74 65 64 20 67 72 61 70 68 2e 0a 0a 20 20 20 20 41 20 60 73 69 6d 70 6c 65 20	.directed.graph.......A.`simple.
80e0	63 79 63 6c 65 60 2c 20 6f 72 20 60 65 6c 65 6d 65 6e 74 61 72 79 20 63 69 72 63 75 69 74 60 2c	cycle`,.or.`elementary.circuit`,
8100	20 69 73 20 61 20 63 6c 6f 73 65 64 20 70 61 74 68 20 77 68 65 72 65 0a 20 20 20 20 6e 6f 20 6e	.is.a.closed.path.where.....no.n
8120	6f 64 65 20 61 70 70 65 61 72 73 20 74 77 69 63 65 2e 20 54 77 6f 20 65 6c 65 6d 65 6e 74 61 72	ode.appears.twice..Two.elementar
8140	79 20 63 69 72 63 75 69 74 73 20 61 72 65 20 64 69 73 74 69 6e 63 74 20 69 66 20 74 68 65 79 0a	y.circuits.are.distinct.if.they.
8160	20 20 20 20 61 72 65 20 6e 6f 74 20 63 79 63 6c 69 63 20 70 65 72 6d 75 74 61 74 69 6f 6e 73 20	....are.not.cyclic.permutations.
8180	6f 66 20 65 61 63 68 20 6f 74 68 65 72 2e 0a 0a 20 20 20 20 54 68 69 73 20 76 65 72 73 69 6f 6e	of.each.other.......This.version
81a0	20 75 73 65 73 20 61 20 72 65 63 75 72 73 69 76 65 20 61 6c 67 6f 72 69 74 68 6d 20 74 6f 20 62	.uses.a.recursive.algorithm.to.b
81c0	75 69 6c 64 20 61 20 6c 69 73 74 20 6f 66 20 63 79 63 6c 65 73 2e 0a 20 20 20 20 59 6f 75 20 73	uild.a.list.of.cycles......You.s
81e0	68 6f 75 6c 64 20 70 72 6f 62 61 62 6c 79 20 75 73 65 20 74 68 65 20 69 74 65 72 61 74 6f 72 20	hould.probably.use.the.iterator.
8200	76 65 72 73 69 6f 6e 20 63 61 6c 6c 65 64 20 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 28 29 2e 0a	version.called.simple_cycles()..
8220	20 20 20 20 57 61 72 6e 69 6e 67 3a 20 54 68 69 73 20 72 65 63 75 72 73 69 76 65 20 76 65 72 73	....Warning:.This.recursive.vers
8240	69 6f 6e 20 75 73 65 73 20 6c 6f 74 73 20 6f 66 20 52 41 4d 21 0a 20 20 20 20 49 74 20 61 70 70	ion.uses.lots.of.RAM!.....It.app
8260	65 61 72 73 20 69 6e 20 4e 65 74 77 6f 72 6b 58 20 66 6f 72 20 70 65 64 61 67 6f 67 69 63 61 6c	ears.in.NetworkX.for.pedagogical
8280	20 76 61 6c 75 65 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d	.value.......Parameters.....----
82a0	2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 20 3a 20 4e 65 74 77 6f 72 6b 58 20 44 69 47 72 61 70 68 0a	------.....G.:.NetworkX.DiGraph.
82c0	20 20 20 20 20 20 20 41 20 64 69 72 65 63 74 65 64 20 67 72 61 70 68 0a 0a 20 20 20 20 52 65 74	.......A.directed.graph......Ret
82e0	75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 41 20 6c 69 73 74 20 6f 66 20 63	urns.....-------.....A.list.of.c
8300	79 63 6c 65 73 2c 20 77 68 65 72 65 20 65 61 63 68 20 63 79 63 6c 65 20 69 73 20 72 65 70 72 65	ycles,.where.each.cycle.is.repre
8320	73 65 6e 74 65 64 20 62 79 20 61 20 6c 69 73 74 20 6f 66 20 6e 6f 64 65 73 0a 20 20 20 20 61 6c	sented.by.a.list.of.nodes.....al
8340	6f 6e 67 20 74 68 65 20 63 79 63 6c 65 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 3a 0a 0a 20 20	ong.the.cycle.......Example:....
8360	20 20 3e 3e 3e 20 65 64 67 65 73 20 3d 20 5b 28 30 2c 20 30 29 2c 20 28 30 2c 20 31 29 2c 20 28	..>>>.edges.=.[(0,.0),.(0,.1),.(
8380	30 2c 20 32 29 2c 20 28 31 2c 20 32 29 2c 20 28 32 2c 20 30 29 2c 20 28 32 2c 20 31 29 2c 20 28	0,.2),.(1,.2),.(2,.0),.(2,.1),.(
83a0	32 2c 20 32 29 5d 0a 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 44 69 47 72 61 70 68 28 65 64	2,.2)].....>>>.G.=.nx.DiGraph(ed
83c0	67 65 73 29 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 72 65 63 75 72 73 69 76 65 5f 73 69 6d 70 6c 65	ges).....>>>.nx.recursive_simple
83e0	5f 63 79 63 6c 65 73 28 47 29 0a 20 20 20 20 5b 5b 30 5d 2c 20 5b 32 5d 2c 20 5b 30 2c 20 31 2c	_cycles(G).....[[0],.[2],.[0,.1,
8400	20 32 5d 2c 20 5b 30 2c 20 32 5d 2c 20 5b 31 2c 20 32 5d 5d 0a 0a 20 20 20 20 4e 6f 74 65 73 0a	.2],.[0,.2],.[1,.2]]......Notes.
8420	20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 54 68 65 20 69 6d 70 6c 65 6d 65 6e 74 61 74 69 6f 6e	....-----.....The.implementation
8440	20 66 6f 6c 6c 6f 77 73 20 70 70 2e 20 37 39 2d 38 30 20 69 6e 20 5b 31 5d 5f 2e 0a 0a 20 20 20	.follows.pp..79-80.in.[1]_......
8460	20 54 68 65 20 74 69 6d 65 20 63 6f 6d 70 6c 65 78 69 74 79 20 69 73 20 24 4f 28 28 6e 2b 65 29	.The.time.complexity.is.$O((n+e)
8480	28 63 2b 31 29 29 24 20 66 6f 72 20 24 6e 24 20 6e 6f 64 65 73 2c 20 24 65 24 20 65 64 67 65 73	(c+1))$.for.$n$.nodes,.$e$.edges
84a0	20 61 6e 64 20 24 63 24 0a 20 20 20 20 65 6c 65 6d 65 6e 74 61 72 79 20 63 69 72 63 75 69 74 73	.and.$c$.....elementary.circuits
84c0	2e 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d	.......References.....----------
84e0	0a 20 20 20 20 2e 2e 20 5b 31 5d 20 46 69 6e 64 69 6e 67 20 61 6c 6c 20 74 68 65 20 65 6c 65 6d	........[1].Finding.all.the.elem
8500	65 6e 74 61 72 79 20 63 69 72 63 75 69 74 73 20 6f 66 20 61 20 64 69 72 65 63 74 65 64 20 67 72	entary.circuits.of.a.directed.gr
8520	61 70 68 2e 0a 20 20 20 20 20 20 20 44 2e 20 42 2e 20 4a 6f 68 6e 73 6f 6e 2c 20 53 49 41 4d 20	aph.........D..B..Johnson,.SIAM.
8540	4a 6f 75 72 6e 61 6c 20 6f 6e 20 43 6f 6d 70 75 74 69 6e 67 20 34 2c 20 6e 6f 2e 20 31 2c 20 37	Journal.on.Computing.4,.no..1,.7
8560	37 2d 38 34 2c 20 31 39 37 35 2e 0a 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 64 6f 69 2e 6f	7-84,.1975.........https://doi.o
8580	72 67 2f 31 30 2e 31 31 33 37 2f 30 32 30 34 30 30 37 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f	rg/10.1137/0204007......See.Also
85a0	0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 2c	.....--------.....simple_cycles,
85c0	20 63 79 63 6c 65 5f 62 61 73 69 73 0a 20 20 20 20 63 01 00 00 00 00 00 00 00 00 00 00 00 04 00	.cycle_basis.....c..............
85e0	00 00 13 00 00 00 f3 66 00 00 00 95 03 97 00 89 03 7c 00 19 00 00 00 72 2b 64 01 89 03 7c 00 3c	.......f.........|.....r+d...|.<
8600	00 00 00 89 01 7c 00 19 00 00 00 72 20 02 00 89 02 89 01 7c 00 19 00 00 00 6a 01 00 00 00 00 00	.....|.....r.......|.....j......
8620	00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 01 00 89	................................
8640	01 7c 00 19 00 00 00 72 01 8c 1f 79 02 79 02 79 02 29 03 7a 36 52 65 63 75 72 73 69 76 65 6c 79	.|.....r...y.y.y.).z6Recursively
8660	20 75 6e 62 6c 6f 63 6b 20 61 6e 64 20 72 65 6d 6f 76 65 20 6e 6f 64 65 73 20 66 72 6f 6d 20 42	.unblock.and.remove.nodes.from.B
8680	5b 74 68 69 73 6e 6f 64 65 5d 2e 46 4e 29 01 72 17 00 00 00 29 04 da 08 74 68 69 73 6e 6f 64 65	[thisnode].FN).r....)...thisnode
86a0	72 84 00 00 00 da 08 5f 75 6e 62 6c 6f 63 6b 72 83 00 00 00 73 04 00 00 00 20 80 80 80 72 28 00	r......_unblockr....s........r(.
86c0	00 00 72 be 00 00 00 7a 29 72 65 63 75 72 73 69 76 65 5f 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73	..r....z)recursive_simple_cycles
86e0	2e 3c 6c 6f 63 61 6c 73 3e 2e 5f 75 6e 62 6c 6f 63 6b 33 03 00 00 73 3d 00 00 00 f8 80 00 e0 0b	.<locals>._unblock3...s=........
8700	12 90 38 d2 0b 1c d8 20 25 88 47 90 48 d1 0c 1d d8 12 13 90 48 92 2b d9 10 18 98 11 98 38 99 1b	..8.....%.G.H.......H.+......8..
8720	9f 1f 99 1f d3 19 2a d4 10 2b f0 03 00 13 14 90 48 95 2b f0 05 00 0c 1d 72 29 00 00 00 63 03 00	......*..+......H.+.....r)...c..
8740	00 00 00 00 00 00 00 00 00 00 06 00 00 00 13 00 00 00 f3 2c 01 00 00 95 06 97 00 64 01 7d 03 89	...................,.......d.}..
8760	09 6a 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 01	.j...................|..........
8780	00 64 02 89 07 7c 00 3c 00 00 00 7c 02 7c 00 19 00 00 00 44 00 5d 31 00 00 7d 04 7c 04 7c 01 6b	.d...|.<...|.|.....D.]1..}.|.|.k
87a0	28 00 00 72 17 89 0a 6a 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 89 09 64 00 64	(..r...j.....................d.d
87c0	00 1a 00 ab 01 00 00 00 00 00 00 01 00 64 02 7d 03 8c 1f 89 07 7c 04 19 00 00 00 72 01 8c 25 02	.............d.}.....|.....r..%.
87e0	00 89 08 7c 04 7c 01 7c 02 ab 03 00 00 00 00 00 00 73 01 8c 30 64 02 7d 03 8c 33 04 00 7c 03 72	...|.|.|.........s..0d.}..3..|.r
8800	09 02 00 89 06 7c 00 ab 01 00 00 00 00 00 00 01 00 6e 26 7c 02 7c 00 19 00 00 00 44 00 5d 1e 00	.....|...........n&|.|.....D.]..
8820	00 7d 04 7c 00 89 05 7c 04 19 00 00 00 76 01 73 01 8c 0b 89 05 7c 04 19 00 00 00 6a 01 00 00 00	.}.|...|.....v.s.....|.....j....
8840	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 01 00 8c 20 04 00 89	...............|................
8860	09 6a 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 01 00 7c	.j.............................|
8880	03 53 00 29 03 4e 46 54 29 02 72 18 00 00 00 72 17 00 00 00 29 0b 72 bd 00 00 00 da 09 73 74 61	.S.).NFT).r....r....).r......sta
88a0	72 74 6e 6f 64 65 da 09 63 6f 6d 70 6f 6e 65 6e 74 72 86 00 00 00 da 08 6e 65 78 74 6e 6f 64 65	rtnode..componentr......nextnode
88c0	72 84 00 00 00 72 be 00 00 00 72 83 00 00 00 da 07 63 69 72 63 75 69 74 72 82 00 00 00 da 06 72	r....r....r......circuitr......r
88e0	65 73 75 6c 74 73 0b 00 00 00 20 20 20 20 20 80 80 80 80 80 80 72 28 00 00 00 72 c3 00 00 00 7a	esults...............r(...r....z
8900	28 72 65 63 75 72 73 69 76 65 5f 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 2e 3c 6c 6f 63 61 6c 73	(recursive_simple_cycles.<locals
8920	3e 2e 63 69 72 63 75 69 74 3a 03 00 00 73 b7 00 00 00 f8 80 00 d8 11 16 88 06 d8 08 0c 8f 0b 89	>.circuit:...s..................
8940	0b 90 48 d4 08 1d d8 1c 20 88 07 90 08 d1 08 19 d8 18 21 a0 28 d1 18 2b f2 00 06 09 22 88 48 d8	..H...............!.(..+....".H.
8960	0f 17 98 39 d2 0f 24 d8 10 16 97 0d 91 0d 98 64 a1 31 98 67 d4 10 26 d8 19 1d 91 06 d8 15 1c 98	...9..$........d.1.g..&.........
8980	58 d3 15 26 d9 13 1a 98 38 a0 59 b0 09 d5 13 3a d8 1d 21 91 46 f0 0d 06 09 22 f1 0e 00 0c 12 d9	X..&....8.Y....:..!.F...."......
89a0	0c 14 90 58 d5 0c 1e e0 1c 25 a0 68 d1 1c 2f f2 00 02 0d 31 90 08 d8 13 1b a0 31 a0 58 a1 3b d2	...X.....%.h../....1......1.X.;.
89c0	13 2e d8 14 15 90 68 91 4b d7 14 26 d1 14 26 a0 78 d5 14 30 f0 05 02 0d 31 f0 06 00 09 0d 8f 08	......h.K..&..&.x..0....1.......
89e0	89 08 8c 0a d8 0f 15 88 0d 72 29 00 00 00 63 01 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 33	.........r)...c................3
8a00	00 00 00 f3 3a 00 00 00 95 02 4b 00 01 00 97 00 7c 00 5d 12 00 00 7d 01 89 02 7c 01 19 00 00 00	....:.....K.....|.]...}...|.....
8a20	89 02 89 03 19 00 00 00 6b 5c 00 00 73 01 8c 0f 7c 01 96 01 97 01 01 00 8c 14 04 00 79 00 ad 03	........k\..s...|...........y...
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90c0	ab 01 00 00 00 00 00 00 01 00 7c 0a 6a 15 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00	..........|.j...................
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9100	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 09 ab 01 00 00 00 00 00 00 01 00 8c ee	..................|.............
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9180	74 1f 00 00 00 00 00 00 00 00 7c 05 ab 01 00 00 00 00 00 00 44 00 5d 17 00 00 5c 02 00 00 7d 12	t.........|.........D.]...\...}.
91a0	7d 0c 02 00 7f 03 7c 0c ab 01 00 00 00 00 00 00 5c 02 00 00 7d 0d 7d 0e 7c 0d 7c 06 6b 28 00 00	}.....|.........\...}.}.|.|.k(..
91c0	73 01 8c 17 01 00 6e 01 04 00 7c 05 7f 12 64 07 1a 00 53 00 23 00 74 0e 00 00 00 00 00 00 00 00	s.....n...|...d...S.#.t.........
91e0	24 00 72 08 01 00 67 00 7d 08 7c 0d 68 01 7d 0a 59 00 8c d0 77 00 78 03 59 00 77 01 29 0c 61 14	$.r...g.}.|.h.}.Y...w.x.Y.w.).a.
9200	0b 00 00 52 65 74 75 72 6e 73 20 61 20 63 79 63 6c 65 20 66 6f 75 6e 64 20 76 69 61 20 64 65 70	...Returns.a.cycle.found.via.dep
9220	74 68 2d 66 69 72 73 74 20 74 72 61 76 65 72 73 61 6c 2e 0a 0a 20 20 20 20 54 68 65 20 63 79 63	th-first.traversal.......The.cyc
9240	6c 65 20 69 73 20 61 20 6c 69 73 74 20 6f 66 20 65 64 67 65 73 20 69 6e 64 69 63 61 74 69 6e 67	le.is.a.list.of.edges.indicating
9260	20 74 68 65 20 63 79 63 6c 69 63 20 70 61 74 68 2e 0a 20 20 20 20 4f 72 69 65 6e 74 61 74 69 6f	.the.cyclic.path......Orientatio
9280	6e 20 6f 66 20 64 69 72 65 63 74 65 64 20 65 64 67 65 73 20 69 73 20 63 6f 6e 74 72 6f 6c 6c 65	n.of.directed.edges.is.controlle
92a0	64 20 62 79 20 60 6f 72 69 65 6e 74 61 74 69 6f 6e 60 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74	d.by.`orientation`.......Paramet
92c0	65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 20 3a 20 67 72 61 70 68	ers.....----------.....G.:.graph
92e0	0a 20 20 20 20 20 20 20 20 41 20 64 69 72 65 63 74 65 64 2f 75 6e 64 69 72 65 63 74 65 64 20 67	.........A.directed/undirected.g
9300	72 61 70 68 2f 6d 75 6c 74 69 67 72 61 70 68 2e 0a 0a 20 20 20 20 73 6f 75 72 63 65 20 3a 20 6e	raph/multigraph.......source.:.n
9320	6f 64 65 2c 20 6c 69 73 74 20 6f 66 20 6e 6f 64 65 73 0a 20 20 20 20 20 20 20 20 54 68 65 20 6e	ode,.list.of.nodes.........The.n
9340	6f 64 65 20 66 72 6f 6d 20 77 68 69 63 68 20 74 68 65 20 74 72 61 76 65 72 73 61 6c 20 62 65 67	ode.from.which.the.traversal.beg
9360	69 6e 73 2e 20 49 66 20 4e 6f 6e 65 2c 20 74 68 65 6e 20 61 20 73 6f 75 72 63 65 0a 20 20 20 20	ins..If.None,.then.a.source.....
9380	20 20 20 20 69 73 20 63 68 6f 73 65 6e 20 61 72 62 69 74 72 61 72 69 6c 79 20 61 6e 64 20 72 65	....is.chosen.arbitrarily.and.re
93a0	70 65 61 74 65 64 6c 79 20 75 6e 74 69 6c 20 61 6c 6c 20 65 64 67 65 73 20 66 72 6f 6d 20 65 61	peatedly.until.all.edges.from.ea
93c0	63 68 20 6e 6f 64 65 20 69 6e 0a 20 20 20 20 20 20 20 20 74 68 65 20 67 72 61 70 68 20 61 72 65	ch.node.in.........the.graph.are
93e0	20 73 65 61 72 63 68 65 64 2e 0a 0a 20 20 20 20 6f 72 69 65 6e 74 61 74 69 6f 6e 20 3a 20 4e 6f	.searched.......orientation.:.No
9400	6e 65 20 7c 20 27 6f 72 69 67 69 6e 61 6c 27 20 7c 20 27 72 65 76 65 72 73 65 27 20 7c 20 27 69	ne.|.'original'.|.'reverse'.|.'i
9420	67 6e 6f 72 65 27 20 28 64 65 66 61 75 6c 74 3a 20 4e 6f 6e 65 29 0a 20 20 20 20 20 20 20 20 46	gnore'.(default:.None).........F
9440	6f 72 20 64 69 72 65 63 74 65 64 20 67 72 61 70 68 73 20 61 6e 64 20 64 69 72 65 63 74 65 64 20	or.directed.graphs.and.directed.
9460	6d 75 6c 74 69 67 72 61 70 68 73 2c 20 65 64 67 65 20 74 72 61 76 65 72 73 61 6c 73 20 6e 65 65	multigraphs,.edge.traversals.nee
9480	64 20 6e 6f 74 0a 20 20 20 20 20 20 20 20 72 65 73 70 65 63 74 20 74 68 65 20 6f 72 69 67 69 6e	d.not.........respect.the.origin
94a0	61 6c 20 6f 72 69 65 6e 74 61 74 69 6f 6e 20 6f 66 20 74 68 65 20 65 64 67 65 73 2e 0a 20 20 20	al.orientation.of.the.edges.....
94c0	20 20 20 20 20 57 68 65 6e 20 73 65 74 20 74 6f 20 27 72 65 76 65 72 73 65 27 20 65 76 65 72 79	.....When.set.to.'reverse'.every
94e0	20 65 64 67 65 20 69 73 20 74 72 61 76 65 72 73 65 64 20 69 6e 20 74 68 65 20 72 65 76 65 72 73	.edge.is.traversed.in.the.revers
9500	65 20 64 69 72 65 63 74 69 6f 6e 2e 0a 20 20 20 20 20 20 20 20 57 68 65 6e 20 73 65 74 20 74 6f	e.direction..........When.set.to
9520	20 27 69 67 6e 6f 72 65 27 2c 20 65 76 65 72 79 20 65 64 67 65 20 69 73 20 74 72 65 61 74 65 64	.'ignore',.every.edge.is.treated
9540	20 61 73 20 75 6e 64 69 72 65 63 74 65 64 2e 0a 20 20 20 20 20 20 20 20 57 68 65 6e 20 73 65 74	.as.undirected..........When.set
9560	20 74 6f 20 27 6f 72 69 67 69 6e 61 6c 27 2c 20 65 76 65 72 79 20 65 64 67 65 20 69 73 20 74 72	.to.'original',.every.edge.is.tr
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95c0	74 75 70 6c 65 73 20 61 64 64 20 61 20 6c 61 73 74 20 65 6e 74 72 79 20 74 6f 0a 20 20 20 20 20	tuples.add.a.last.entry.to......
95e0	20 20 20 69 6e 64 69 63 61 74 65 20 74 68 65 20 64 69 72 65 63 74 69 6f 6e 20 69 6e 20 77 68 69	...indicate.the.direction.in.whi
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9620	20 20 20 20 49 66 20 6f 72 69 65 6e 74 61 74 69 6f 6e 20 69 73 20 4e 6f 6e 65 2c 20 74 68 65 20	....If.orientation.is.None,.the.
9640	79 69 65 6c 64 65 64 20 65 64 67 65 20 68 61 73 20 6e 6f 20 64 69 72 65 63 74 69 6f 6e 20 69 6e	yielded.edge.has.no.direction.in
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96e0	74 20 6f 66 20 64 69 72 65 63 74 65 64 20 65 64 67 65 73 20 69 6e 64 69 63 61 74 69 6e 67 20 74	t.of.directed.edges.indicating.t
9700	68 65 20 70 61 74 68 20 74 61 6b 65 6e 20 66 6f 72 20 74 68 65 20 6c 6f 6f 70 2e 0a 20 20 20 20	he.path.taken.for.the.loop......
9720	20 20 20 20 49 66 20 6e 6f 20 63 79 63 6c 65 20 69 73 20 66 6f 75 6e 64 2c 20 74 68 65 6e 20 61	....If.no.cycle.is.found,.then.a
9740	6e 20 65 78 63 65 70 74 69 6f 6e 20 69 73 20 72 61 69 73 65 64 2e 0a 20 20 20 20 20 20 20 20 46	n.exception.is.raised..........F
9760	6f 72 20 67 72 61 70 68 73 2c 20 61 6e 20 65 64 67 65 20 69 73 20 6f 66 20 74 68 65 20 66 6f 72	or.graphs,.an.edge.is.of.the.for
9780	6d 20 60 28 75 2c 20 76 29 60 20 77 68 65 72 65 20 60 75 60 20 61 6e 64 20 60 76 60 0a 20 20 20	m.`(u,.v)`.where.`u`.and.`v`....
97a0	20 20 20 20 20 61 72 65 20 74 68 65 20 74 61 69 6c 20 61 6e 64 20 68 65 61 64 20 6f 66 20 74 68	.....are.the.tail.and.head.of.th
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9800	61 6e 20 65 64 67 65 20 69 73 20 6f 66 20 74 68 65 20 66 6f 72 6d 20 60 28 75 2c 20 76 2c 20 6b	an.edge.is.of.the.form.`(u,.v,.k
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9860	20 69 73 20 64 69 72 65 63 74 65 64 2c 20 74 68 65 6e 20 60 75 60 20 61 6e 64 20 60 76 60 0a 20	.is.directed,.then.`u`.and.`v`..
9880	20 20 20 20 20 20 20 61 72 65 20 61 6c 77 61 79 73 20 69 6e 20 74 68 65 20 6f 72 64 65 72 20 6f	.......are.always.in.the.order.o
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98c0	20 20 20 20 49 66 20 6f 72 69 65 6e 74 61 74 69 6f 6e 20 69 73 20 6e 6f 74 20 4e 6f 6e 65 20 74	....If.orientation.is.not.None.t
98e0	68 65 6e 20 74 68 65 20 65 64 67 65 20 74 75 70 6c 65 20 69 73 20 65 78 74 65 6e 64 65 64 20 74	hen.the.edge.tuple.is.extended.t
9900	6f 20 69 6e 63 6c 75 64 65 0a 20 20 20 20 20 20 20 20 74 68 65 20 64 69 72 65 63 74 69 6f 6e 20	o.include.........the.direction.
9920	6f 66 20 74 72 61 76 65 72 73 61 6c 20 28 27 66 6f 72 77 61 72 64 27 20 6f 72 20 27 72 65 76 65	of.traversal.('forward'.or.'reve
9940	72 73 65 27 29 20 6f 6e 20 74 68 61 74 20 65 64 67 65 2e 0a 0a 20 20 20 20 52 61 69 73 65 73 0a	rse').on.that.edge.......Raises.
9960	20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 4e 65 74 77 6f 72 6b 58 4e 6f 43 79 63 6c 65 0a 20	....------.....NetworkXNoCycle..
9980	20 20 20 20 20 20 20 49 66 20 6e 6f 20 63 79 63 6c 65 20 77 61 73 20 66 6f 75 6e 64 2e 0a 0a 20	.......If.no.cycle.was.found....
99a0	20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 49 6e 20	...Examples.....--------.....In.
99c0	74 68 69 73 20 65 78 61 6d 70 6c 65 2c 20 77 65 20 63 6f 6e 73 74 72 75 63 74 20 61 20 44 41 47	this.example,.we.construct.a.DAG
99e0	20 61 6e 64 20 66 69 6e 64 2c 20 69 6e 20 74 68 65 20 66 69 72 73 74 20 63 61 6c 6c 2c 20 74 68	.and.find,.in.the.first.call,.th
9a00	61 74 20 74 68 65 72 65 0a 20 20 20 20 61 72 65 20 6e 6f 20 64 69 72 65 63 74 65 64 20 63 79 63	at.there.....are.no.directed.cyc
9a20	6c 65 73 2c 20 61 6e 64 20 73 6f 20 61 6e 20 65 78 63 65 70 74 69 6f 6e 20 69 73 20 72 61 69 73	les,.and.so.an.exception.is.rais
9a40	65 64 2e 20 49 6e 20 74 68 65 20 73 65 63 6f 6e 64 20 63 61 6c 6c 2c 0a 20 20 20 20 77 65 20 69	ed..In.the.second.call,.....we.i
9a60	67 6e 6f 72 65 20 65 64 67 65 20 6f 72 69 65 6e 74 61 74 69 6f 6e 73 20 61 6e 64 20 66 69 6e 64	gnore.edge.orientations.and.find
9a80	20 74 68 61 74 20 74 68 65 72 65 20 69 73 20 61 6e 20 75 6e 64 69 72 65 63 74 65 64 20 63 79 63	.that.there.is.an.undirected.cyc
9aa0	6c 65 2e 0a 20 20 20 20 4e 6f 74 65 20 74 68 61 74 20 74 68 65 20 73 65 63 6f 6e 64 20 63 61 6c	le......Note.that.the.second.cal
9ac0	6c 20 66 69 6e 64 73 20 61 20 64 69 72 65 63 74 65 64 20 63 79 63 6c 65 20 77 68 69 6c 65 20 65	l.finds.a.directed.cycle.while.e
9ae0	66 66 65 63 74 69 76 65 6c 79 0a 20 20 20 20 74 72 61 76 65 72 73 69 6e 67 20 61 6e 20 75 6e 64	ffectively.....traversing.an.und
9b00	69 72 65 63 74 65 64 20 67 72 61 70 68 2c 20 61 6e 64 20 73 6f 2c 20 77 65 20 66 6f 75 6e 64 20	irected.graph,.and.so,.we.found.
9b20	61 6e 20 22 75 6e 64 69 72 65 63 74 65 64 20 63 79 63 6c 65 22 2e 0a 20 20 20 20 54 68 69 73 20	an."undirected.cycle"......This.
9b40	6d 65 61 6e 73 20 74 68 61 74 20 74 68 69 73 20 44 41 47 20 73 74 72 75 63 74 75 72 65 20 64 6f	means.that.this.DAG.structure.do
9b60	65 73 20 6e 6f 74 20 66 6f 72 6d 20 61 20 64 69 72 65 63 74 65 64 20 74 72 65 65 20 28 77 68 69	es.not.form.a.directed.tree.(whi
9b80	63 68 0a 20 20 20 20 69 73 20 61 6c 73 6f 20 6b 6e 6f 77 6e 20 61 73 20 61 20 70 6f 6c 79 74 72	ch.....is.also.known.as.a.polytr
9ba0	65 65 29 2e 0a 0a 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 44 69 47 72 61 70 68 28 5b 28 30	ee).......>>>.G.=.nx.DiGraph([(0
9bc0	2c 20 31 29 2c 20 28 30 2c 20 32 29 2c 20 28 31 2c 20 32 29 5d 29 0a 20 20 20 20 3e 3e 3e 20 6e	,.1),.(0,.2),.(1,.2)]).....>>>.n
9be0	78 2e 66 69 6e 64 5f 63 79 63 6c 65 28 47 2c 20 6f 72 69 65 6e 74 61 74 69 6f 6e 3d 22 6f 72 69	x.find_cycle(G,.orientation="ori
9c00	67 69 6e 61 6c 22 29 0a 20 20 20 20 54 72 61 63 65 62 61 63 6b 20 28 6d 6f 73 74 20 72 65 63 65	ginal").....Traceback.(most.rece
9c20	6e 74 20 63 61 6c 6c 20 6c 61 73 74 29 3a 0a 20 20 20 20 20 20 20 20 2e 2e 2e 0a 20 20 20 20 6e	nt.call.last):.................n
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9c60	65 3a 20 4e 6f 20 63 79 63 6c 65 20 66 6f 75 6e 64 2e 0a 20 20 20 20 3e 3e 3e 20 6c 69 73 74 28	e:.No.cycle.found......>>>.list(
9c80	6e 78 2e 66 69 6e 64 5f 63 79 63 6c 65 28 47 2c 20 6f 72 69 65 6e 74 61 74 69 6f 6e 3d 22 69 67	nx.find_cycle(G,.orientation="ig
9ca0	6e 6f 72 65 22 29 29 0a 20 20 20 20 5b 28 30 2c 20 31 2c 20 27 66 6f 72 77 61 72 64 27 29 2c 20	nore")).....[(0,.1,.'forward'),.
9cc0	28 31 2c 20 32 2c 20 27 66 6f 72 77 61 72 64 27 29 2c 20 28 30 2c 20 32 2c 20 27 72 65 76 65 72	(1,.2,.'forward'),.(0,.2,.'rever
9ce0	73 65 27 29 5d 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d	se')]......See.Also.....--------
9d00	0a 20 20 20 20 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 0a 20 20 20 20 29 02 4e da 08 6f 72 69 67	.....simple_cycles.....).N..orig
9d20	69 6e 61 6c 63 01 00 00 00 00 00 00 00 00 00 00 00 03 00 00 00 13 00 00 00 f3 0c 00 00 00 97 00	inalc...........................
9d40	7c 00 64 00 64 01 1a 00 53 00 29 02 4e 72 46 00 00 00 72 2e 00 00 00 a9 01 da 04 65 64 67 65 73	|.d.d...S.).NrF...r........edges
9d60	01 00 00 00 20 72 28 00 00 00 da 08 74 61 69 6c 68 65 61 64 7a 1c 66 69 6e 64 5f 63 79 63 6c 65	.....r(.....tailheadz.find_cycle
9d80	2e 3c 6c 6f 63 61 6c 73 3e 2e 74 61 69 6c 68 65 61 64 b6 03 00 00 73 0d 00 00 00 80 00 d8 13 17	.<locals>.tailhead....s.........
9da0	98 02 98 11 90 38 88 4f 72 29 00 00 00 da 07 72 65 76 65 72 73 65 63 01 00 00 00 00 00 00 00 00	.....8.Or).....reversec.........
9dc0	00 00 00 03 00 00 00 13 00 00 00 f3 16 00 00 00 97 00 7c 00 64 01 19 00 00 00 7c 00 64 02 19 00	..................|.d.....|.d...
9de0	00 00 66 02 53 00 29 03 4e 72 35 00 00 00 72 02 00 00 00 72 2e 00 00 00 72 d9 00 00 00 73 01 00	..f.S.).Nr5...r....r....r....s..
9e00	00 00 20 72 28 00 00 00 72 db 00 00 00 7a 1c 66 69 6e 64 5f 63 79 63 6c 65 2e 3c 6c 6f 63 61 6c	...r(...r....z.find_cycle.<local
9e20	73 3e 2e 74 61 69 6c 68 65 61 64 bb 03 00 00 73 15 00 00 00 80 00 d8 13 17 98 01 91 37 98 44 a0	s>.tailhead....s............7.D.
9e40	11 99 47 d0 13 23 d0 0c 23 72 29 00 00 00 da 06 69 67 6e 6f 72 65 63 01 00 00 00 00 00 00 00 00	..G..#..#r).....ignorec.........
9e60	00 00 00 03 00 00 00 13 00 00 00 f3 30 00 00 00 97 00 7c 00 64 01 19 00 00 00 64 02 6b 28 00 00	............0.....|.d.....d.k(..
9e80	72 0a 7c 00 64 03 19 00 00 00 7c 00 64 04 19 00 00 00 66 02 53 00 7c 00 64 00 64 05 1a 00 53 00	r.|.d.....|.d.....f.S.|.d.d...S.
9ea0	29 06 4e 72 7e 00 00 00 72 dc 00 00 00 72 35 00 00 00 72 02 00 00 00 72 46 00 00 00 72 2e 00 00	).Nr~...r....r5...r....rF...r...
9ec0	00 72 d9 00 00 00 73 01 00 00 00 20 72 28 00 00 00 72 db 00 00 00 7a 1c 66 69 6e 64 5f 63 79 63	.r....s.....r(...r....z.find_cyc
9ee0	6c 65 2e 3c 6c 6f 63 61 6c 73 3e 2e 74 61 69 6c 68 65 61 64 c0 03 00 00 73 2c 00 00 00 80 00 d8	le.<locals>.tailhead....s,......
9f00	0f 13 90 42 89 78 98 39 d2 0f 24 d8 17 1b 98 41 91 77 a0 04 a0 51 a1 07 d0 17 27 d0 10 27 d8 13	...B.x.9..$....A.w...Q....'..'..
9f20	17 98 02 98 11 90 38 88 4f 72 29 00 00 00 4e 72 35 00 00 00 72 7e 00 00 00 72 02 00 00 00 7a 0f	......8.Or)...Nr5...r~...r....z.
9f40	4e 6f 20 63 79 63 6c 65 20 66 6f 75 6e 64 2e 29 10 72 4b 00 00 00 72 16 00 00 00 da 0b 6e 62 75	No.cycle.found.).rK...r......nbu
9f60	6e 63 68 5f 69 74 65 72 72 4f 00 00 00 da 08 65 64 67 65 5f 64 66 73 72 17 00 00 00 72 7f 00 00	nch_iterrO.....edge_dfsr....r...
9f80	00 da 0a 49 6e 64 65 78 45 72 72 6f 72 72 18 00 00 00 72 65 00 00 00 72 19 00 00 00 72 80 00 00	...IndexErrorr....re...r....r...
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9fc0	6c 65 da 09 65 6e 75 6d 65 72 61 74 65 29 13 72 1a 00 00 00 da 06 73 6f 75 72 63 65 da 0b 6f 72	le..enumerate).r......source..or
9fe0	69 65 6e 74 61 74 69 6f 6e 72 db 00 00 00 da 08 65 78 70 6c 6f 72 65 64 72 25 00 00 00 da 0a 66	ientationr......exploredr%.....f
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a260	07 88 01 88 34 d9 15 1d 98 64 93 5e 89 0a 88 04 88 64 d8 0b 0f 90 3a d3 0b 1d d9 0c 11 f0 07 03	....4....d.^.....d....:.........
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a2a0	05 d8 28 2c a0 76 98 0c d9 18 1d f0 07 03 15 1e fa 73 12 00 00 00 c2 0e 10 46 11 04 c6 11 0e 46	..(,.v...........s.......F.....F
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a2e0	00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 03 00 00 00 f3 58 00 00 00 87 00 87 01 97 00 74 01	....................X.........t.
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a320	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 89 00 ab 01 00 00 00 00 00 00 44 00 ab 00 00 00	..........................D.....
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a380	47 0a 0a 20 20 20 20 4d 69 6e 69 6d 75 6d 20 77 65 69 67 68 74 20 6d 65 61 6e 73 20 61 20 63 79	G......Minimum.weight.means.a.cy
a3a0	63 6c 65 20 62 61 73 69 73 20 66 6f 72 20 77 68 69 63 68 20 74 68 65 20 74 6f 74 61 6c 20 77 65	cle.basis.for.which.the.total.we
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a400	69 6d 75 6d 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d	imum.......Parameters.....------
a420	2d 2d 2d 2d 0a 20 20 20 20 47 20 3a 20 4e 65 74 77 6f 72 6b 58 20 47 72 61 70 68 0a 20 20 20 20	----.....G.:.NetworkX.Graph.....
a440	77 65 69 67 68 74 3a 20 73 74 72 69 6e 67 0a 20 20 20 20 20 20 20 20 6e 61 6d 65 20 6f 66 20 74	weight:.string.........name.of.t
a460	68 65 20 65 64 67 65 20 61 74 74 72 69 62 75 74 65 20 74 6f 20 75 73 65 20 66 6f 72 20 65 64 67	he.edge.attribute.to.use.for.edg
a480	65 20 77 65 69 67 68 74 73 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d	e.weights......Returns.....-----
a4a0	2d 2d 0a 20 20 20 20 41 20 6c 69 73 74 20 6f 66 20 63 79 63 6c 65 20 6c 69 73 74 73 2e 20 20 45	--.....A.list.of.cycle.lists...E
a4c0	61 63 68 20 63 79 63 6c 65 20 6c 69 73 74 20 69 73 20 61 20 6c 69 73 74 20 6f 66 20 6e 6f 64 65	ach.cycle.list.is.a.list.of.node
a4e0	73 0a 20 20 20 20 77 68 69 63 68 20 66 6f 72 6d 73 20 61 20 63 79 63 6c 65 20 28 6c 6f 6f 70 29	s.....which.forms.a.cycle.(loop)
a500	20 69 6e 20 47 2e 20 4e 6f 74 65 20 74 68 61 74 20 74 68 65 20 6e 6f 64 65 73 20 61 72 65 20 6e	.in.G..Note.that.the.nodes.are.n
a520	6f 74 0a 20 20 20 20 6e 65 63 65 73 73 61 72 69 6c 79 20 72 65 74 75 72 6e 65 64 20 69 6e 20 61	ot.....necessarily.returned.in.a
a540	20 6f 72 64 65 72 20 62 79 20 77 68 69 63 68 20 74 68 65 79 20 61 70 70 65 61 72 20 69 6e 20 74	.order.by.which.they.appear.in.t
a560	68 65 20 63 79 63 6c 65 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d	he.cycle......Examples.....-----
a580	2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 47 72 61 70 68 28 29 0a 20 20 20 20 3e	---.....>>>.G.=.nx.Graph().....>
a5a0	3e 3e 20 6e 78 2e 61 64 64 5f 63 79 63 6c 65 28 47 2c 20 5b 30 2c 20 31 2c 20 32 2c 20 33 5d 29	>>.nx.add_cycle(G,.[0,.1,.2,.3])
a5c0	0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 61 64 64 5f 63 79 63 6c 65 28 47 2c 20 5b 30 2c 20 33 2c 20	.....>>>.nx.add_cycle(G,.[0,.3,.
a5e0	34 2c 20 35 5d 29 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 6d 69 6e 69 6d 75 6d 5f 63 79 63 6c 65 5f	4,.5]).....>>>.nx.minimum_cycle_
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a620	32 2c 20 31 2c 20 30 5d 5d 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 3a 0a 20 20 20 20 20	2,.1,.0]]......References:......
a640	20 20 20 5b 31 5d 20 4b 61 76 69 74 68 61 2c 20 54 65 6c 69 6b 65 70 61 6c 6c 69 2c 20 65 74 20	...[1].Kavitha,.Telikepalli,.et.
a660	61 6c 2e 20 22 41 6e 20 4f 28 6d 5e 32 6e 29 20 41 6c 67 6f 72 69 74 68 6d 20 66 6f 72 0a 20 20	al.."An.O(m^2n).Algorithm.for...
a680	20 20 20 20 20 20 4d 69 6e 69 6d 75 6d 20 43 79 63 6c 65 20 42 61 73 69 73 20 6f 66 20 47 72 61	......Minimum.Cycle.Basis.of.Gra
a6a0	70 68 73 2e 22 0a 20 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6c 69 6e 6b 2e 73 70 72 69 6e 67	phs.".........http://link.spring
a6c0	65 72 2e 63 6f 6d 2f 61 72 74 69 63 6c 65 2f 31 30 2e 31 30 30 37 2f 73 30 30 34 35 33 2d 30 30	er.com/article/10.1007/s00453-00
a6e0	37 2d 39 30 36 34 2d 7a 0a 20 20 20 20 20 20 20 20 5b 32 5d 20 64 65 20 50 69 6e 61 2c 20 4a 2e	7-9064-z.........[2].de.Pina,.J.
a700	20 31 39 39 35 2e 20 41 70 70 6c 69 63 61 74 69 6f 6e 73 20 6f 66 20 73 68 6f 72 74 65 73 74 20	.1995..Applications.of.shortest.
a720	70 61 74 68 20 6d 65 74 68 6f 64 73 2e 0a 20 20 20 20 20 20 20 20 50 68 2e 44 2e 20 74 68 65 73	path.methods..........Ph.D..thes
a740	69 73 2c 20 55 6e 69 76 65 72 73 69 74 79 20 6f 66 20 41 6d 73 74 65 72 64 61 6d 2c 20 4e 65 74	is,.University.of.Amsterdam,.Net
a760	68 65 72 6c 61 6e 64 73 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d	herlands......See.Also.....-----
a780	2d 2d 2d 0a 20 20 20 20 73 69 6d 70 6c 65 5f 63 79 63 6c 65 73 2c 20 63 79 63 6c 65 5f 62 61 73	---.....simple_cycles,.cycle_bas
a7a0	69 73 0a 20 20 20 20 63 01 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 33 00 00 00 f3 54 00 00	is.....c................3....T..
a7c0	00 95 02 4b 00 01 00 97 00 7c 00 5d 1f 00 00 7d 01 74 01 00 00 00 00 00 00 00 00 89 02 6a 03 00	...K.....|.]...}.t...........j..
a7e0	00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 89 03 ab 02 00	.................|..............
a800	00 00 00 00 00 96 01 97 01 01 00 8c 21 04 00 79 00 ad 03 77 01 72 2d 00 00 00 29 02 da 10 5f 6d	............!..y...w.r-...)..._m
a820	69 6e 5f 63 79 63 6c 65 5f 62 61 73 69 73 72 5f 00 00 00 29 04 72 30 00 00 00 72 5b 00 00 00 72	in_cycle_basisr_...).r0...r[...r
a840	1a 00 00 00 72 f4 00 00 00 73 04 00 00 00 20 20 80 80 72 28 00 00 00 72 33 00 00 00 7a 26 6d 69	....r....s........r(...r3...z&mi
a860	6e 69 6d 75 6d 5f 63 79 63 6c 65 5f 62 61 73 69 73 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65	nimum_cycle_basis.<locals>.<gene
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a8a0	2a a0 51 9b 2d a8 16 d7 09 30 d1 08 55 f9 73 04 00 00 00 83 25 28 01 29 03 da 03 73 75 6d 72 4f	*.Q.-....0..U.s.....%(.)...sumrO
a8c0	00 00 00 da 14 63 6f 6e 6e 65 63 74 65 64 5f 63 6f 6d 70 6f 6e 65 6e 74 73 29 02 72 1a 00 00 00	.....connected_components).r....
a8e0	72 f4 00 00 00 73 02 00 00 00 60 60 72 28 00 00 00 72 0d 00 00 00 72 0d 00 00 00 10 04 00 00 73	r....s....``r(...r....r........s
a900	2a 00 00 00 f9 80 00 f4 52 01 00 0c 0f dc 08 55 bc 22 d7 3a 51 d1 3a 51 d0 52 53 d3 3a 54 d4 08	*.......R......U.".:Q.:Q.RS.:T..
a920	55 d8 08 0a f3 05 03 0c 06 f0 00 03 05 06 72 29 00 00 00 63 02 00 00 00 00 00 00 00 00 00 00 00	U.............r)...c............
a940	0c 00 00 00 03 00 00 00 f3 5e 02 00 00 87 0b 97 00 67 00 7d 02 74 01 00 00 00 00 00 00 00 00 74	.........^.......g.}.t.........t
a960	03 00 00 00 00 00 00 00 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 64	.........j...................|.d
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aa80	04 ab 01 00 00 00 00 00 00 01 00 7c 08 44 00 8f 0b 87 0b 8f 0c 63 03 67 00 63 02 5d 5c 00 00 8a	...........|.D.......c.g.c.]\...
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abc0	00 00 00 00 00 00 00 00 00 05 00 00 00 33 00 00 00 f3 3e 00 00 00 95 01 4b 00 01 00 97 00 7c 00	.............3....>.....K.....|.
abe0	5d 14 00 00 7d 01 7c 01 89 02 76 00 78 01 73 0a 01 00 7c 01 64 00 64 00 64 01 85 03 19 00 00 00	]...}.|...v.x.s...|.d.d.d.......
ac00	89 02 76 00 96 01 97 01 01 00 8c 16 04 00 79 00 ad 03 77 01 72 9d 00 00 00 72 2e 00 00 00 29 03	..v...........y...w.r....r....).
ac20	72 30 00 00 00 72 9e 00 00 00 da 04 6f 72 74 68 73 03 00 00 00 20 20 80 72 28 00 00 00 72 33 00	r0...r......orths.......r(...r3.
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