summaryrefslogtreecommitdiff
path: root/.venv/lib/python3.12/site-packages/networkx/algorithms/__pycache__/cluster.cpython-312.pyc
blob: 92872f5246338cf221e3d083357c52d721b32b6a (plain)
ofshex dumpascii
0000 cb 0d 0d 0a 00 00 00 00 85 fa a7 68 ef 57 00 00 e3 00 00 00 00 00 00 00 00 00 00 00 00 04 00 00 ...........h.W..................
0020 00 00 00 00 00 f3 e2 01 00 00 97 00 64 00 5a 00 64 01 64 02 6c 01 6d 02 5a 02 01 00 64 01 64 03 ............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 5a 07 64 01 64 05 6c 08 6d 09 5a 09 01 00 l.m.Z.m.Z...d.d.l.Z.d.d.l.m.Z...
0060 67 00 64 06 a2 01 5a 0a 02 00 65 09 64 07 ab 01 00 00 00 00 00 00 65 07 6a 16 00 00 00 00 00 00 g.d...Z...e.d.........e.j.......
0080 00 00 00 00 00 00 00 00 00 00 00 00 64 15 64 08 84 01 ab 00 00 00 00 00 00 00 ab 00 00 00 00 00 ............d.d.................
00a0 00 00 5a 0c 02 00 65 09 64 09 ab 01 00 00 00 00 00 00 64 15 64 0a 84 01 ab 00 00 00 00 00 00 00 ..Z...e.d.........d.d...........
00c0 5a 0d 02 00 65 09 64 09 ab 01 00 00 00 00 00 00 64 16 64 0c 84 01 ab 00 00 00 00 00 00 00 5a 0e Z...e.d.........d.d...........Z.
00e0 02 00 65 09 64 09 ab 01 00 00 00 00 00 00 64 15 64 0d 84 01 ab 00 00 00 00 00 00 00 5a 0f 02 00 ..e.d.........d.d...........Z...
0100 65 09 64 09 ab 01 00 00 00 00 00 00 64 16 64 0e 84 01 ab 00 00 00 00 00 00 00 5a 10 02 00 65 07 e.d.........d.d...........Z...e.
0120 6a 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 0b ac 0f ab 01 00 00 00 00 00 00 j...................d...........
0140 64 17 64 10 84 01 ab 00 00 00 00 00 00 00 5a 11 02 00 65 07 6a 16 00 00 00 00 00 00 00 00 00 00 d.d...........Z...e.j...........
0160 00 00 00 00 00 00 00 00 64 0b ac 0f ab 01 00 00 00 00 00 00 64 18 64 11 84 01 ab 00 00 00 00 00 ........d...........d.d.........
0180 00 00 5a 12 65 07 6a 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 12 84 00 ab 00 ..Z.e.j...................d.....
01a0 00 00 00 00 00 00 5a 13 65 07 6a 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 15 ......Z.e.j...................d.
01c0 64 13 84 01 ab 00 00 00 00 00 00 00 5a 14 02 00 65 09 64 07 ab 01 00 00 00 00 00 00 65 07 6a 16 d...........Z...e.d.........e.j.
01e0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 15 64 14 84 01 ab 00 00 00 00 00 00 00 ..................d.d...........
0200 ab 00 00 00 00 00 00 00 5a 15 79 04 29 19 7a 3e 41 6c 67 6f 72 69 74 68 6d 73 20 74 6f 20 63 68 ........Z.y.).z>Algorithms.to.ch
0220 61 72 61 63 74 65 72 69 7a 65 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 74 72 69 61 6e 67 6c aracterize.the.number.of.triangl
0240 65 73 20 69 6e 20 61 20 67 72 61 70 68 2e e9 00 00 00 00 29 01 da 07 43 6f 75 6e 74 65 72 29 02 es.in.a.graph......)...Counter).
0260 da 05 63 68 61 69 6e da 0c 63 6f 6d 62 69 6e 61 74 69 6f 6e 73 4e 29 01 da 13 6e 6f 74 5f 69 6d ..chain..combinationsN)...not_im
0280 70 6c 65 6d 65 6e 74 65 64 5f 66 6f 72 29 06 da 09 74 72 69 61 6e 67 6c 65 73 da 12 61 76 65 72 plemented_for)...triangles..aver
02a0 61 67 65 5f 63 6c 75 73 74 65 72 69 6e 67 da 0a 63 6c 75 73 74 65 72 69 6e 67 da 0c 74 72 61 6e age_clustering..clustering..tran
02c0 73 69 74 69 76 69 74 79 da 11 73 71 75 61 72 65 5f 63 6c 75 73 74 65 72 69 6e 67 da 12 67 65 6e sitivity..square_clustering..gen
02e0 65 72 61 6c 69 7a 65 64 5f 64 65 67 72 65 65 da 08 64 69 72 65 63 74 65 64 63 02 00 00 00 00 00 eralized_degree..directedc......
0300 00 00 00 00 00 00 0a 00 00 00 03 00 00 00 f3 2e 02 00 00 97 00 7c 01 81 48 7c 01 7c 00 76 00 72 .....................|..H|.|.v.r
0320 1b 74 01 00 00 00 00 00 00 00 00 74 03 00 00 00 00 00 00 00 00 7c 00 7c 01 ab 02 00 00 00 00 00 .t.........t.........|.|........
0340 00 ab 01 00 00 00 00 00 00 64 01 19 00 00 00 64 01 7a 02 00 00 53 00 74 03 00 00 00 00 00 00 00 .........d.....d.z...S.t........
0360 00 7c 00 7c 01 ab 02 00 00 00 00 00 00 44 00 8f 02 8f 03 8f 04 8f 05 63 05 69 00 63 02 5d 0d 00 .|.|.........D.........c.i.c.]..
0380 00 5c 04 00 00 7d 02 7d 03 7d 04 7d 05 7c 02 7c 04 64 01 7a 02 00 00 93 02 8c 0f 04 00 63 05 7d .\...}.}.}.}.|.|.d.z.........c.}
03a0 05 7d 04 7d 03 7d 02 53 00 69 00 7d 06 7c 00 6a 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .}.}.}.S.i.}.|.j................
03c0 00 00 00 ab 00 00 00 00 00 00 00 44 00 5d 23 00 00 5c 02 00 00 7d 07 7d 08 7c 08 44 00 8f 09 63 ...........D.]#..\...}.}.|.D...c
03e0 02 68 00 63 02 5d 0f 00 00 7d 09 7c 09 7c 06 76 01 73 01 8c 08 7c 09 7c 07 6b 37 00 00 73 01 8c .h.c.]...}.|.|.v.s...|.|.k7..s..
0400 0e 7c 09 92 02 8c 11 04 00 63 02 7d 09 7c 06 7c 07 3c 00 00 00 8c 25 04 00 74 07 00 00 00 00 00 .|.......c.}.|.|.<....%..t......
0420 00 00 00 74 08 00 00 00 00 00 00 00 00 6a 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ...t.........j..................
0440 00 7c 00 64 02 ab 02 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7d 0a 7c 06 6a 0d 00 00 00 00 00 .|.d.................}.|.j......
0460 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 44 00 5d 4a 00 00 5c 02 00 00 7d .....................D.]J..\...}
0480 0b 7d 08 7c 08 44 00 5d 40 00 00 7d 0c 7c 08 7c 06 7c 0c 19 00 00 00 7a 01 00 00 7d 0d 74 0f 00 .}.|.D.]@..}.|.|.|.....z...}.t..
04a0 00 00 00 00 00 00 00 7c 0d ab 01 00 00 00 00 00 00 7d 0e 7c 0a 7c 0b 78 02 78 02 19 00 00 00 7c .......|.........}.|.|.x.x.....|
04c0 0e 7a 0d 00 00 63 03 63 02 3c 00 00 00 7c 0a 7c 0c 78 02 78 02 19 00 00 00 7c 0e 7a 0d 00 00 63 .z...c.c.<...|.|.x.x.....|.z...c
04e0 03 63 02 3c 00 00 00 7c 0a 6a 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0d ab .c.<...|.j...................|..
0500 01 00 00 00 00 00 00 01 00 8c 42 04 00 8c 4c 04 00 74 09 00 00 00 00 00 00 00 00 7c 0a ab 01 00 ..........B...L..t.........|....
0520 00 00 00 00 00 53 00 63 02 01 00 63 05 7d 05 7d 04 7d 03 7d 02 77 00 63 02 01 00 63 02 7d 09 77 .....S.c...c.}.}.}.}.w.c...c.}.w
0540 00 29 03 61 da 03 00 00 43 6f 6d 70 75 74 65 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 74 72 .).a....Compute.the.number.of.tr
0560 69 61 6e 67 6c 65 73 2e 0a 0a 20 20 20 20 46 69 6e 64 73 20 74 68 65 20 6e 75 6d 62 65 72 20 6f iangles.......Finds.the.number.o
0580 66 20 74 72 69 61 6e 67 6c 65 73 20 74 68 61 74 20 69 6e 63 6c 75 64 65 20 61 20 6e 6f 64 65 20 f.triangles.that.include.a.node.
05a0 61 73 20 6f 6e 65 20 76 65 72 74 65 78 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 as.one.vertex.......Parameters..
05c0 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 0a 20 20 20 20 ...----------.....G.:.graph.....
05e0 20 20 20 41 20 6e 65 74 77 6f 72 6b 78 20 67 72 61 70 68 0a 0a 20 20 20 20 6e 6f 64 65 73 20 3a ...A.networkx.graph......nodes.:
0600 20 6e 6f 64 65 2c 20 69 74 65 72 61 62 6c 65 20 6f 66 20 6e 6f 64 65 73 2c 20 6f 72 20 4e 6f 6e .node,.iterable.of.nodes,.or.Non
0620 65 20 28 64 65 66 61 75 6c 74 3d 4e 6f 6e 65 29 0a 20 20 20 20 20 20 20 20 49 66 20 61 20 73 69 e.(default=None).........If.a.si
0640 6e 67 6c 65 74 6f 6e 20 6e 6f 64 65 2c 20 72 65 74 75 72 6e 20 74 68 65 20 6e 75 6d 62 65 72 20 ngleton.node,.return.the.number.
0660 6f 66 20 74 72 69 61 6e 67 6c 65 73 20 66 6f 72 20 74 68 61 74 20 6e 6f 64 65 2e 0a 20 20 20 20 of.triangles.for.that.node......
0680 20 20 20 20 49 66 20 61 6e 20 69 74 65 72 61 62 6c 65 2c 20 63 6f 6d 70 75 74 65 20 74 68 65 20 ....If.an.iterable,.compute.the.
06a0 6e 75 6d 62 65 72 20 6f 66 20 74 72 69 61 6e 67 6c 65 73 20 66 6f 72 20 65 61 63 68 20 6f 66 20 number.of.triangles.for.each.of.
06c0 74 68 6f 73 65 20 6e 6f 64 65 73 2e 0a 20 20 20 20 20 20 20 20 49 66 20 60 4e 6f 6e 65 60 20 28 those.nodes..........If.`None`.(
06e0 74 68 65 20 64 65 66 61 75 6c 74 29 20 63 6f 6d 70 75 74 65 20 74 68 65 20 6e 75 6d 62 65 72 20 the.default).compute.the.number.
0700 6f 66 20 74 72 69 61 6e 67 6c 65 73 20 66 6f 72 20 61 6c 6c 20 6e 6f 64 65 73 20 69 6e 20 60 47 of.triangles.for.all.nodes.in.`G
0720 60 2e 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 `.......Returns.....-------.....
0740 6f 75 74 20 3a 20 64 69 63 74 20 6f 72 20 69 6e 74 0a 20 20 20 20 20 20 20 49 66 20 60 6e 6f 64 out.:.dict.or.int........If.`nod
0760 65 73 60 20 69 73 20 61 20 63 6f 6e 74 61 69 6e 65 72 20 6f 66 20 6e 6f 64 65 73 2c 20 72 65 74 es`.is.a.container.of.nodes,.ret
0780 75 72 6e 73 20 6e 75 6d 62 65 72 20 6f 66 20 74 72 69 61 6e 67 6c 65 73 20 6b 65 79 65 64 20 62 urns.number.of.triangles.keyed.b
07a0 79 20 6e 6f 64 65 20 28 64 69 63 74 29 2e 0a 20 20 20 20 20 20 20 49 66 20 60 6e 6f 64 65 73 60 y.node.(dict).........If.`nodes`
07c0 20 69 73 20 61 20 73 70 65 63 69 66 69 63 20 6e 6f 64 65 2c 20 72 65 74 75 72 6e 73 20 6e 75 6d .is.a.specific.node,.returns.num
07e0 62 65 72 20 6f 66 20 74 72 69 61 6e 67 6c 65 73 20 66 6f 72 20 74 68 65 20 6e 6f 64 65 20 28 69 ber.of.triangles.for.the.node.(i
0800 6e 74 29 2e 0a 0a 20 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 nt).......Examples.....--------.
0820 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 63 6f 6d 70 6c 65 74 65 5f 67 72 61 70 68 28 35 29 ....>>>.G.=.nx.complete_graph(5)
0840 0a 20 20 20 20 3e 3e 3e 20 70 72 69 6e 74 28 6e 78 2e 74 72 69 61 6e 67 6c 65 73 28 47 2c 20 30 .....>>>.print(nx.triangles(G,.0
0860 29 29 0a 20 20 20 20 36 0a 20 20 20 20 3e 3e 3e 20 70 72 69 6e 74 28 6e 78 2e 74 72 69 61 6e 67 )).....6.....>>>.print(nx.triang
0880 6c 65 73 28 47 29 29 0a 20 20 20 20 7b 30 3a 20 36 2c 20 31 3a 20 36 2c 20 32 3a 20 36 2c 20 33 les(G)).....{0:.6,.1:.6,.2:.6,.3
08a0 3a 20 36 2c 20 34 3a 20 36 7d 0a 20 20 20 20 3e 3e 3e 20 70 72 69 6e 74 28 6c 69 73 74 28 6e 78 :.6,.4:.6}.....>>>.print(list(nx
08c0 2e 74 72 69 61 6e 67 6c 65 73 28 47 2c 20 5b 30 2c 20 31 5d 29 2e 76 61 6c 75 65 73 28 29 29 29 .triangles(G,.[0,.1]).values()))
08e0 0a 20 20 20 20 5b 36 2c 20 36 5d 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d .....[6,.6]......Notes.....-----
0900 0a 20 20 20 20 53 65 6c 66 20 6c 6f 6f 70 73 20 61 72 65 20 69 67 6e 6f 72 65 64 2e 0a 0a 20 20 .....Self.loops.are.ignored.....
0920 20 20 e9 02 00 00 00 72 02 00 00 00 29 09 da 04 6e 65 78 74 da 1a 5f 74 72 69 61 6e 67 6c 65 73 .......r....)...next.._triangles
0940 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 da 09 61 64 6a 61 63 65 6e 63 79 72 03 00 00 00 _and_degree_iter..adjacencyr....
0960 da 04 64 69 63 74 da 08 66 72 6f 6d 6b 65 79 73 da 05 69 74 65 6d 73 da 03 6c 65 6e da 06 75 70 ..dict..fromkeys..items..len..up
0980 64 61 74 65 29 0f da 01 47 da 05 6e 6f 64 65 73 da 01 76 da 01 64 da 01 74 da 01 5f da 0a 6c 61 date)...G..nodes..v..d..t.._..la
09a0 74 65 72 5f 6e 62 72 73 da 04 6e 6f 64 65 da 09 6e 65 69 67 68 62 6f 72 73 da 01 6e da 0f 74 72 ter_nbrs..node..neighbors..n..tr
09c0 69 61 6e 67 6c 65 5f 63 6f 75 6e 74 73 da 05 6e 6f 64 65 31 da 05 6e 6f 64 65 32 da 0b 74 68 69 iangle_counts..node1..node2..thi
09e0 72 64 5f 6e 6f 64 65 73 da 01 6d 73 0f 00 00 00 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 fa rd_nodes..ms....................
0a00 62 2f 68 6f 6d 65 2f 62 6c 61 63 6b 68 61 6f 2f 75 69 75 63 2d 63 6f 75 72 73 65 2d 67 72 61 70 b/home/blackhao/uiuc-course-grap
0a20 68 2f 2e 76 65 6e 76 2f 6c 69 62 2f 70 79 74 68 6f 6e 33 2e 31 32 2f 73 69 74 65 2d 70 61 63 6b h/.venv/lib/python3.12/site-pack
0a40 61 67 65 73 2f 6e 65 74 77 6f 72 6b 78 2f 61 6c 67 6f 72 69 74 68 6d 73 2f 63 6c 75 73 74 65 72 ages/networkx/algorithms/cluster
0a60 2e 70 79 72 07 00 00 00 72 07 00 00 00 13 00 00 00 73 47 01 00 00 80 00 f0 4c 01 00 08 0d d0 07 .pyr....r........sG......L......
0a80 18 e0 0b 10 90 41 89 3a dc 13 17 d4 18 32 b0 31 b0 65 d3 18 3c d3 13 3d b8 61 d1 13 40 c0 41 d1 .....A.:.....2.1.e..<..=.a..@.A.
0aa0 13 45 d0 0c 45 f4 08 00 2d 47 01 c0 71 c8 25 d3 2c 50 d7 0f 51 d1 0f 51 99 6a 98 61 a0 11 a0 41 .E..E...-G..q.%.,P..Q..Q.j.a...A
0ac0 a0 71 90 01 90 31 98 01 91 36 91 09 d5 0f 51 d0 08 51 f0 0c 00 12 14 80 4a f0 06 00 1c 1d 9f 3b .q...1...6....Q..Q......J......;
0ae0 99 3b 9b 3d f2 00 01 05 57 01 89 0f 88 04 88 69 d8 27 30 d6 1b 56 a0 21 b0 41 b8 5a d2 34 47 c8 .;.=....W......i.'0..V.!.A.Z.4G.
0b00 41 d0 51 55 cb 49 9a 41 d2 1b 56 88 0a 90 34 d2 08 18 f0 03 01 05 57 01 f4 0a 00 17 1e 9c 64 9f A.QU.I.A..V...4.......W.......d.
0b20 6d 99 6d a8 41 a8 71 d3 1e 31 d3 16 32 80 4f d8 1c 26 d7 1c 2c d1 1c 2c d3 1c 2e f2 00 06 05 30 m.m.A.q..1..2.O..&..,..,.......0
0b40 d1 08 18 88 05 88 79 d8 15 1e f2 00 05 09 30 88 45 d8 1a 23 a0 6a b0 15 d1 26 37 d1 1a 37 88 4b ......y.......0.E..#.j...&7..7.K
0b60 dc 10 13 90 4b d3 10 20 88 41 d8 0c 1b 98 45 d3 0c 22 a0 61 d1 0c 27 d3 0c 22 d8 0c 1b 98 45 d3 ....K....A....E..".a..'.."....E.
0b80 0c 22 a0 61 d1 0c 27 d3 0c 22 d8 0c 1b d7 0c 22 d1 0c 22 a0 3b d5 0c 2f f1 0b 05 09 30 f0 03 06 .".a..'.."....."..".;../....0...
0ba0 05 30 f4 10 00 0c 10 90 0f d3 0b 20 d0 04 20 f9 f5 2f 00 10 52 01 f9 f2 14 00 1c 57 01 73 17 00 .0.............../..R......W.s..
0bc0 00 00 b3 12 44 0a 0a c1 27 09 44 12 06 c1 31 05 44 12 06 c1 37 04 44 12 06 da 0a 6d 75 6c 74 69 ....D...'.D...1.D...7.D....multi
0be0 67 72 61 70 68 63 02 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 23 00 00 00 f3 3c 01 00 00 87 graphc................#....<....
0c00 00 87 07 4b 00 01 00 97 00 7c 01 80 1b 89 00 6a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ...K.....|.....j................
0c20 00 00 00 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 7d ...j...........................}
0c40 02 6e 1a 88 00 66 01 64 02 84 08 89 00 6a 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .n...f.d.....j..................
0c60 00 7c 01 ab 01 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 7d 02 7c 02 44 00 5d 5a 00 00 5c .|.........D.........}.|.D.]Z..\
0c80 02 00 00 7d 03 7d 04 74 07 00 00 00 00 00 00 00 00 7c 04 ab 01 00 00 00 00 00 00 7c 03 68 01 7a ...}.}.t.........|.........|.h.z
0ca0 0a 00 00 8a 07 74 09 00 00 00 00 00 00 00 00 88 00 88 07 66 02 64 03 84 08 89 07 44 00 ab 00 00 .....t.............f.d.....D....
0cc0 00 00 00 00 00 ab 01 00 00 00 00 00 00 7d 05 74 0b 00 00 00 00 00 00 00 00 64 04 84 00 7c 05 6a .............}.t.........d...|.j
0ce0 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 44 00 ab 00 00 ...........................D....
0d00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7d 06 7c 03 74 0d 00 00 00 00 00 00 00 00 89 07 ab 01 00 .............}.|.t..............
0d20 00 00 00 00 00 7c 06 7c 05 66 04 96 01 97 01 01 00 8c 5c 04 00 79 01 ad 03 77 01 29 05 7a e4 52 .....|.|.f........\..y...w.).z.R
0d40 65 74 75 72 6e 20 61 6e 20 69 74 65 72 61 74 6f 72 20 6f 66 20 28 6e 6f 64 65 2c 20 64 65 67 72 eturn.an.iterator.of.(node,.degr
0d60 65 65 2c 20 74 72 69 61 6e 67 6c 65 73 2c 20 67 65 6e 65 72 61 6c 69 7a 65 64 20 64 65 67 72 65 ee,.triangles,.generalized.degre
0d80 65 29 2e 0a 0a 20 20 20 20 54 68 69 73 20 64 6f 75 62 6c 65 20 63 6f 75 6e 74 73 20 74 72 69 61 e).......This.double.counts.tria
0da0 6e 67 6c 65 73 20 73 6f 20 79 6f 75 20 6d 61 79 20 77 61 6e 74 20 74 6f 20 64 69 76 69 64 65 20 ngles.so.you.may.want.to.divide.
0dc0 62 79 20 32 2e 0a 20 20 20 20 53 65 65 20 64 65 67 72 65 65 28 29 2c 20 74 72 69 61 6e 67 6c 65 by.2......See.degree(),.triangle
0de0 73 28 29 20 61 6e 64 20 67 65 6e 65 72 61 6c 69 7a 65 64 5f 64 65 67 72 65 65 28 29 20 66 6f 72 s().and.generalized_degree().for
0e00 20 64 65 66 69 6e 69 74 69 6f 6e 73 0a 20 20 20 20 61 6e 64 20 64 65 74 61 69 6c 73 2e 0a 0a 20 .definitions.....and.details....
0e20 20 20 20 4e 63 01 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 33 00 00 00 f3 2c 00 00 00 95 01 ...Nc................3....,.....
0e40 4b 00 01 00 97 00 7c 00 5d 0b 00 00 7d 01 7c 01 89 02 7c 01 19 00 00 00 66 02 96 01 97 01 01 00 K.....|.]...}.|...|.....f.......
0e60 8c 0d 04 00 79 00 ad 03 77 01 a9 01 4e a9 00 a9 03 da 02 2e 30 72 21 00 00 00 72 18 00 00 00 73 ....y...w...N.......0r!...r....s
0e80 03 00 00 00 20 20 80 72 27 00 00 00 fa 09 3c 67 65 6e 65 78 70 72 3e 7a 2d 5f 74 72 69 61 6e 67 .......r'.....<genexpr>z-_triang
0ea0 6c 65 73 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 les_and_degree_iter.<locals>.<ge
0ec0 6e 65 78 70 72 3e 66 00 00 00 f3 19 00 00 00 f8 e8 00 f8 80 00 d2 15 3e a0 41 90 71 98 21 98 41 nexpr>f................>.A.q.!.A
0ee0 99 24 94 69 d1 15 3e f9 f3 04 00 00 00 83 11 14 01 63 01 00 00 00 00 00 00 00 00 00 00 00 08 00 .$.i..>..........c..............
0f00 00 00 33 00 00 00 f3 5a 00 00 00 95 02 4b 00 01 00 97 00 7c 00 5d 22 00 00 7d 01 74 01 00 00 00 ..3....Z.....K.....|.]"..}.t....
0f20 00 00 00 00 00 89 03 74 03 00 00 00 00 00 00 00 00 89 02 7c 01 19 00 00 00 ab 01 00 00 00 00 00 .......t...........|............
0f40 00 7c 01 68 01 7a 0a 00 00 7a 01 00 00 ab 01 00 00 00 00 00 00 96 01 97 01 01 00 8c 24 04 00 79 .|.h.z...z..................$..y
0f60 00 ad 03 77 01 72 2b 00 00 00 29 02 72 16 00 00 00 da 03 73 65 74 29 04 72 2e 00 00 00 da 01 77 ...w.r+...).r......set).r......w
0f80 72 18 00 00 00 da 02 76 73 73 04 00 00 00 20 20 80 80 72 27 00 00 00 72 2f 00 00 00 7a 2d 5f 74 r......vss........r'...r/...z-_t
0fa0 72 69 61 6e 67 6c 65 73 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 2e 3c 6c 6f 63 61 6c 73 riangles_and_degree_iter.<locals
0fc0 3e 2e 3c 67 65 6e 65 78 70 72 3e 6a 00 00 00 73 29 00 00 00 f8 e8 00 f8 80 00 d2 1c 45 b8 51 9c >.<genexpr>j...s)...........E.Q.
0fe0 53 a0 12 a4 73 a8 31 a8 51 a9 34 a3 79 b0 41 b0 33 a1 7f d1 21 37 d7 1d 38 d1 1c 45 f9 73 04 00 S...s.1.Q.4.y.A.3...!7..8..E.s..
1000 00 00 83 28 2b 01 63 01 00 00 00 00 00 00 00 00 00 00 00 03 00 00 00 33 00 00 00 f3 2c 00 00 00 ...(+.c................3....,...
1020 4b 00 01 00 97 00 7c 00 5d 0c 00 00 5c 02 00 00 7d 01 7d 02 7c 01 7c 02 7a 05 00 00 96 01 97 01 K.....|.]...\...}.}.|.|.z.......
1040 01 00 8c 0e 04 00 79 00 ad 03 77 01 72 2b 00 00 00 72 2c 00 00 00 29 03 72 2e 00 00 00 da 01 6b ......y...w.r+...r,...).r......k
1060 da 03 76 61 6c 73 03 00 00 00 20 20 20 72 27 00 00 00 72 2f 00 00 00 7a 2d 5f 74 72 69 61 6e 67 ..vals.......r'...r/...z-_triang
1080 6c 65 73 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 les_and_degree_iter.<locals>.<ge
10a0 6e 65 78 70 72 3e 6b 00 00 00 73 18 00 00 00 e8 00 f8 80 00 d2 18 42 a1 56 a0 51 a8 03 98 11 98 nexpr>k...s...........B.V.Q.....
10c0 53 9d 17 d1 18 42 f9 73 04 00 00 00 82 12 14 01 29 07 da 03 61 64 6a 72 15 00 00 00 da 0b 6e 62 S....B.s........)...adjr......nb
10e0 75 6e 63 68 5f 69 74 65 72 72 33 00 00 00 72 03 00 00 00 da 03 73 75 6d 72 16 00 00 00 29 08 72 unch_iterr3...r......sumr....).r
1100 18 00 00 00 72 19 00 00 00 da 0a 6e 6f 64 65 73 5f 6e 62 72 73 72 1a 00 00 00 da 06 76 5f 6e 62 ....r......nodes_nbrsr......v_nb
1120 72 73 da 0a 67 65 6e 5f 64 65 67 72 65 65 da 0a 6e 74 72 69 61 6e 67 6c 65 73 72 35 00 00 00 73 rs..gen_degree..ntrianglesr5...s
1140 08 00 00 00 60 20 20 20 20 20 20 40 72 27 00 00 00 72 11 00 00 00 72 11 00 00 00 5a 00 00 00 73 ....`......@r'...r....r....Z...s
1160 8f 00 00 00 f9 e8 00 f8 80 00 f0 12 00 08 0d 80 7d d8 15 16 97 55 91 55 97 5b 91 5b 93 5d 89 0a ................}....U.U.[.[.]..
1180 e3 15 3e a8 11 af 1d a9 1d b0 75 d3 29 3d d4 15 3e 88 0a e0 15 1f f2 00 04 05 33 89 09 88 01 88 ..>.......u.)=..>.........3.....
11a0 36 dc 0d 10 90 16 8b 5b 98 41 98 33 d1 0d 1e 88 02 dc 15 1c d4 1c 45 c0 22 d4 1c 45 d3 15 45 88 6......[.A.3..........E."..E..E.
11c0 0a dc 15 18 d1 18 42 a8 7a d7 2f 3f d1 2f 3f d3 2f 41 d4 18 42 d3 15 42 88 0a d8 0f 10 94 23 90 ......B.z./?./?./A..B..B......#.
11e0 62 93 27 98 3a a0 7a d0 0e 32 d3 08 32 f1 09 04 05 33 f9 73 06 00 00 00 84 42 18 42 1c 01 da 06 b.'.:.z..2..2....3.s.....B.B....
1200 77 65 69 67 68 74 63 03 00 00 00 00 00 00 00 00 00 00 00 0d 00 00 00 23 00 00 00 f3 8c 02 00 00 weightc................#........
1220 87 00 87 02 87 0f 4b 00 01 00 97 00 64 01 64 02 6c 00 7d 03 89 02 81 13 89 00 6a 03 00 00 00 00 ......K.....d.d.l.}.......j.....
1240 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 64 01 6b 28 00 00 72 03 64 03 ......................d.k(..r.d.
1260 8a 0f 6e 24 74 05 00 00 00 00 00 00 00 00 88 02 66 01 64 04 84 08 89 00 6a 07 00 00 00 00 00 00 ..n$t...........f.d.....j.......
1280 00 00 00 00 00 00 00 00 00 00 00 00 64 05 ac 06 ab 01 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 ............d...........D.......
12a0 00 00 ab 01 00 00 00 00 00 00 8a 0f 7c 01 80 1b 89 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 ............|.....j.............
12c0 00 00 00 00 00 00 6a 0b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 ......j.........................
12e0 00 00 7d 04 6e 1a 88 00 66 01 64 07 84 08 89 00 6a 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ..}.n...f.d.....j...............
1300 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 7d 04 88 00 88 0f 88 02 ....|.........D.........}.......
1320 66 03 64 08 84 08 7d 05 7c 04 44 00 5d b5 00 00 5c 02 00 00 7d 06 7d 07 74 0f 00 00 00 00 00 00 f.d...}.|.D.]...\...}.}.t.......
1340 00 00 7c 07 ab 01 00 00 00 00 00 00 7c 06 68 01 7a 0a 00 00 7d 08 64 01 7d 09 74 0f 00 00 00 00 ..|.........|.h.z...}.d.}.t.....
1360 00 00 00 00 ab 00 00 00 00 00 00 00 7d 0a 7c 08 44 00 5d 74 00 00 7d 0b 7c 0a 6a 11 00 00 00 00 ............}.|.D.]t..}.|.j.....
1380 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 74 0f 00 00 00 00 ..............|...........t.....
13a0 00 00 00 00 89 00 7c 0b 19 00 00 00 ab 01 00 00 00 00 00 00 7c 0a 7a 0a 00 00 7d 0c 02 00 7c 05 ......|.............|.z...}...|.
13c0 7c 06 7c 0b ab 02 00 00 00 00 00 00 7d 0d 7c 09 7c 03 6a 13 00 00 00 00 00 00 00 00 00 00 00 00 |.|.........}.|.|.j.............
13e0 00 00 00 00 00 00 7c 08 7c 0c 7a 01 00 00 44 00 8f 0e 63 02 67 00 63 02 5d 18 00 00 7d 0e 7c 0d ......|.|.z...D...c.g.c.]...}.|.
1400 02 00 7c 05 7c 0b 7c 0e ab 02 00 00 00 00 00 00 7a 05 00 00 02 00 7c 05 7c 0e 7c 06 ab 02 00 00 ..|.|.|.........z.....|.|.|.....
1420 00 00 00 00 7a 05 00 00 91 02 8c 1a 04 00 63 02 7d 0e ab 01 00 00 00 00 00 00 6a 15 00 00 00 00 ....z.........c.}.........j.....
1440 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 7a 0d 00 00 7d 09 8c 76 04 00 ......................z...}..v..
1460 7c 06 74 17 00 00 00 00 00 00 00 00 7c 08 ab 01 00 00 00 00 00 00 64 09 74 19 00 00 00 00 00 00 |.t.........|.........d.t.......
1480 00 00 7c 09 ab 01 00 00 00 00 00 00 7a 05 00 00 66 03 96 01 97 01 01 00 8c b7 04 00 79 02 63 02 ..|.........z...f...........y.c.
14a0 01 00 63 02 7d 0e 77 00 ad 03 77 01 29 0a 61 0f 01 00 00 52 65 74 75 72 6e 20 61 6e 20 69 74 65 ..c.}.w...w.).a....Return.an.ite
14c0 72 61 74 6f 72 20 6f 66 20 28 6e 6f 64 65 2c 20 64 65 67 72 65 65 2c 20 77 65 69 67 68 74 65 64 rator.of.(node,.degree,.weighted
14e0 5f 74 72 69 61 6e 67 6c 65 73 29 2e 0a 0a 20 20 20 20 55 73 65 64 20 66 6f 72 20 77 65 69 67 68 _triangles).......Used.for.weigh
1500 74 65 64 20 63 6c 75 73 74 65 72 69 6e 67 2e 0a 20 20 20 20 4e 6f 74 65 3a 20 74 68 69 73 20 72 ted.clustering......Note:.this.r
1520 65 74 75 72 6e 73 20 74 68 65 20 67 65 6f 6d 65 74 72 69 63 20 61 76 65 72 61 67 65 20 77 65 69 eturns.the.geometric.average.wei
1540 67 68 74 20 6f 66 20 65 64 67 65 73 20 69 6e 20 74 68 65 20 74 72 69 61 6e 67 6c 65 2e 0a 20 20 ght.of.edges.in.the.triangle....
1560 20 20 41 6c 73 6f 2c 20 65 61 63 68 20 74 72 69 61 6e 67 6c 65 20 69 73 20 63 6f 75 6e 74 65 64 ..Also,.each.triangle.is.counted
1580 20 74 77 69 63 65 20 28 65 61 63 68 20 64 69 72 65 63 74 69 6f 6e 29 2e 0a 20 20 20 20 53 6f 20 .twice.(each.direction)......So.
15a0 79 6f 75 20 6d 61 79 20 77 61 6e 74 20 74 6f 20 64 69 76 69 64 65 20 62 79 20 32 2e 0a 0a 20 20 you.may.want.to.divide.by.2.....
15c0 20 20 72 02 00 00 00 4e e9 01 00 00 00 63 01 00 00 00 00 00 00 00 00 00 00 00 05 00 00 00 33 00 ..r....N.....c................3.
15e0 00 00 f3 4a 00 00 00 95 01 4b 00 01 00 97 00 7c 00 5d 1a 00 00 5c 03 00 00 7d 01 7d 02 7d 03 7c ...J.....K.....|.]...\...}.}.}.|
1600 03 6a 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 89 04 64 00 ab 02 00 00 00 00 00 .j.....................d........
1620 00 96 01 97 01 01 00 8c 1c 04 00 79 01 ad 03 77 01 a9 02 72 42 00 00 00 4e a9 01 da 03 67 65 74 ...........y...w...rB...N....get
1640 a9 05 72 2e 00 00 00 da 01 75 72 1a 00 00 00 72 1b 00 00 00 72 40 00 00 00 73 05 00 00 00 20 20 ..r......ur....r....r@...s......
1660 20 20 80 72 27 00 00 00 72 2f 00 00 00 7a 36 5f 77 65 69 67 68 74 65 64 5f 74 72 69 61 6e 67 6c ...r'...r/...z6_weighted_triangl
1680 65 73 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e es_and_degree_iter.<locals>.<gen
16a0 65 78 70 72 3e 7e 00 00 00 f3 22 00 00 00 f8 e8 00 f8 80 00 d2 18 4c a9 67 a8 61 b0 11 b0 41 98 expr>~...."...........L.g.a...A.
16c0 11 9f 15 99 15 98 76 a0 71 d7 19 29 d1 18 4c f9 f3 04 00 00 00 83 20 23 01 54 a9 01 da 04 64 61 ......v.q..)..L........#.T....da
16e0 74 61 63 01 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 33 00 00 00 f3 2c 00 00 00 95 01 4b 00 tac................3....,.....K.
1700 01 00 97 00 7c 00 5d 0b 00 00 7d 01 7c 01 89 02 7c 01 19 00 00 00 66 02 96 01 97 01 01 00 8c 0d ....|.]...}.|...|.....f.........
1720 04 00 79 00 ad 03 77 01 72 2b 00 00 00 72 2c 00 00 00 72 2d 00 00 00 73 03 00 00 00 20 20 80 72 ..y...w.r+...r,...r-...s.......r
1740 27 00 00 00 72 2f 00 00 00 7a 36 5f 77 65 69 67 68 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 5f 61 '...r/...z6_weighted_triangles_a
1760 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 nd_degree_iter.<locals>.<genexpr
1780 3e 82 00 00 00 72 30 00 00 00 72 31 00 00 00 63 02 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 >....r0...r1...c................
17a0 13 00 00 00 f3 3a 00 00 00 95 03 97 00 89 02 7c 00 19 00 00 00 7c 01 19 00 00 00 6a 01 00 00 00 .....:.........|.....|.....j....
17c0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 89 04 64 01 ab 02 00 00 00 00 00 00 89 03 7a 0b 00 .................d...........z..
17e0 00 53 00 a9 02 4e 72 42 00 00 00 72 45 00 00 00 a9 05 72 48 00 00 00 72 1a 00 00 00 72 18 00 00 .S...NrB...rE.....rH...r....r...
1800 00 da 0a 6d 61 78 5f 77 65 69 67 68 74 72 40 00 00 00 73 05 00 00 00 20 20 80 80 80 72 27 00 00 ...max_weightr@...s.........r'..
1820 00 da 02 77 74 7a 2f 5f 77 65 69 67 68 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 5f 61 6e 64 5f 64 ...wtz/_weighted_triangles_and_d
1840 65 67 72 65 65 5f 69 74 65 72 2e 3c 6c 6f 63 61 6c 73 3e 2e 77 74 84 00 00 00 f3 21 00 00 00 f8 egree_iter.<locals>.wt.....!....
1860 80 00 d8 0f 10 90 11 89 74 90 41 89 77 8f 7b 89 7b 98 36 a0 31 d3 0f 25 a8 0a d1 0f 32 d0 08 32 ........t.A.w.{.{.6.1..%....2..2
1880 f3 00 00 00 00 72 0f 00 00 00 29 0d da 05 6e 75 6d 70 79 da 0f 6e 75 6d 62 65 72 5f 6f 66 5f 65 .....r....)...numpy..number_of_e
18a0 64 67 65 73 da 03 6d 61 78 da 05 65 64 67 65 73 72 39 00 00 00 72 15 00 00 00 72 3a 00 00 00 72 dges..max..edgesr9...r....r:...r
18c0 33 00 00 00 da 03 61 64 64 da 04 63 62 72 74 72 3b 00 00 00 72 16 00 00 00 da 05 66 6c 6f 61 74 3.....add..cbrtr;...r......float
18e0 29 10 72 18 00 00 00 72 19 00 00 00 72 40 00 00 00 da 02 6e 70 72 3c 00 00 00 72 52 00 00 00 da ).r....r....r@.....npr<...rR....
1900 01 69 da 04 6e 62 72 73 da 05 69 6e 62 72 73 da 12 77 65 69 67 68 74 65 64 5f 74 72 69 61 6e 67 .i..nbrs..inbrs..weighted_triang
1920 6c 65 73 da 04 73 65 65 6e da 01 6a da 05 6a 6e 62 72 73 da 03 77 69 6a 72 37 00 00 00 72 51 00 les..seen..j..jnbrs..wijr7...rQ.
1940 00 00 73 10 00 00 00 60 20 60 20 20 20 20 20 20 20 20 20 20 20 20 40 72 27 00 00 00 da 23 5f 77 ..s....`.`............@r'....#_w
1960 65 69 67 68 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 eighted_triangles_and_degree_ite
1980 72 72 65 00 00 00 6f 00 00 00 73 3f 01 00 00 fa e8 00 f8 80 00 f3 14 00 05 17 e0 07 0d 80 7e 98 rre...o...s?..................~.
19a0 11 d7 19 2a d1 19 2a d3 19 2c b0 01 d2 19 31 d8 15 16 89 0a e4 15 18 d3 18 4c b8 11 bf 17 b9 17 ...*..*..,....1..........L......
19c0 c0 64 b8 17 d3 39 4b d4 18 4c d3 15 4c 88 0a d8 07 0c 80 7d d8 15 16 97 55 91 55 97 5b 91 5b 93 .d...9K..L..L......}....U.U.[.[.
19e0 5d 89 0a e3 15 3e a8 11 af 1d a9 1d b0 75 d3 29 3d d4 15 3e 88 0a f6 04 01 05 33 f0 06 00 14 1e ]....>.......u.)=..>......3.....
1a00 f2 00 0e 05 3d 89 07 88 01 88 34 dc 10 13 90 44 93 09 98 51 98 43 91 0f 88 05 d8 1d 1e d0 08 1a ....=.....4....D...Q.C..........
1a20 dc 0f 12 8b 75 88 04 d8 11 16 f2 00 09 09 14 88 41 d8 0c 10 8f 48 89 48 90 51 8c 4b e4 14 17 98 ....u...........A....H.H.Q.K....
1a40 01 98 21 99 04 93 49 a0 04 d1 14 24 88 45 f1 06 00 13 15 90 51 98 01 93 28 88 43 d8 0c 1e a0 22 ..!...I....$.E......Q...(.C...."
1a60 a7 27 a1 27 d8 36 3b b8 65 b1 6d d6 10 44 b0 11 90 23 99 02 98 31 98 61 9b 08 91 2e a1 32 a0 61 .'.'.6;.e.m..D...#...1.a.....2.a
1a80 a8 11 a3 38 d3 12 2b d2 10 44 f3 03 02 23 0e e7 0e 11 89 63 8b 65 f1 05 02 0d 14 d1 0c 1e f0 0f ...8..+..D...#.....c.e..........
1aa0 09 09 14 f0 14 00 10 11 94 23 90 65 93 2a 98 61 a4 25 d0 28 3a d3 22 3b d1 1e 3b d0 0e 3c d3 08 .........#.e.*.a.%.(:.";..;..<..
1ac0 3c f1 1d 0e 05 3d f9 f2 18 00 11 45 01 f9 73 12 00 00 00 85 43 25 45 04 01 c3 2a 1d 44 3f 0e c4 <....=.....E..s.....C%E...*.D?..
1ae0 07 3d 45 04 01 63 02 00 00 00 00 00 00 00 00 00 00 00 0d 00 00 00 23 00 00 00 f3 de 01 00 00 87 .=E..c................#.........
1b00 00 4b 00 01 00 97 00 88 00 66 01 64 01 84 08 89 00 6a 01 00 00 00 00 00 00 00 00 00 00 00 00 00 .K.......f.d.....j..............
1b20 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 7d 02 7c 02 44 00 5d .....|.........D.........}.|.D.]
1b40 c9 00 00 5c 03 00 00 7d 03 7d 04 7d 05 74 03 00 00 00 00 00 00 00 00 7c 04 ab 01 00 00 00 00 00 ...\...}.}.}.t.........|........
1b60 00 7c 03 68 01 7a 0a 00 00 7d 06 74 03 00 00 00 00 00 00 00 00 7c 05 ab 01 00 00 00 00 00 00 7c .|.h.z...}.t.........|.........|
1b80 03 68 01 7a 0a 00 00 7d 07 64 02 7d 08 74 05 00 00 00 00 00 00 00 00 7c 06 7c 07 ab 02 00 00 00 .h.z...}.d.}.t.........|.|......
1ba0 00 00 00 44 00 5d 67 00 00 7d 09 74 03 00 00 00 00 00 00 00 00 89 00 6a 06 00 00 00 00 00 00 00 ...D.]g..}.t...........j........
1bc0 00 00 00 00 00 00 00 00 00 00 00 7c 09 19 00 00 00 ab 01 00 00 00 00 00 00 7c 09 68 01 7a 0a 00 ...........|.............|.h.z..
1be0 00 7d 0a 74 03 00 00 00 00 00 00 00 00 89 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .}.t...........j................
1c00 00 00 00 7c 09 19 00 00 00 ab 01 00 00 00 00 00 00 7c 09 68 01 7a 0a 00 00 7d 0b 7c 08 74 0b 00 ...|.............|.h.z...}.|.t..
1c20 00 00 00 00 00 00 00 64 03 84 00 74 05 00 00 00 00 00 00 00 00 7c 06 7c 0a 7a 01 00 00 7c 06 7c .......d...t.........|.|.z...|.|
1c40 0b 7a 01 00 00 7c 07 7c 0a 7a 01 00 00 7c 07 7c 0b 7a 01 00 00 ab 04 00 00 00 00 00 00 44 00 ab .z...|.|.z...|.|.z...........D..
1c60 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7a 0d 00 00 7d 08 8c 69 04 00 74 0d 00 00 00 00 00 ...............z...}..i..t......
1c80 00 00 00 7c 06 ab 01 00 00 00 00 00 00 74 0d 00 00 00 00 00 00 00 00 7c 07 ab 01 00 00 00 00 00 ...|.........t.........|........
1ca0 00 7a 00 00 00 7d 0c 74 0d 00 00 00 00 00 00 00 00 7c 06 7c 07 7a 01 00 00 ab 01 00 00 00 00 00 .z...}.t.........|.|.z..........
1cc0 00 7d 0d 7c 03 7c 0c 7c 0d 7c 08 66 04 96 01 97 01 01 00 8c cb 04 00 79 04 ad 03 77 01 29 05 61 .}.|.|.|.|.f...........y...w.).a
1ce0 03 01 00 00 52 65 74 75 72 6e 20 61 6e 20 69 74 65 72 61 74 6f 72 20 6f 66 0a 20 20 20 20 28 6e ....Return.an.iterator.of.....(n
1d00 6f 64 65 2c 20 74 6f 74 61 6c 5f 64 65 67 72 65 65 2c 20 72 65 63 69 70 72 6f 63 61 6c 5f 64 65 ode,.total_degree,.reciprocal_de
1d20 67 72 65 65 2c 20 64 69 72 65 63 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 29 2e 0a 0a 20 20 20 20 gree,.directed_triangles).......
1d40 55 73 65 64 20 66 6f 72 20 64 69 72 65 63 74 65 64 20 63 6c 75 73 74 65 72 69 6e 67 2e 0a 20 20 Used.for.directed.clustering....
1d60 20 20 4e 6f 74 65 20 74 68 61 74 20 75 6e 6c 69 6b 65 20 60 5f 74 72 69 61 6e 67 6c 65 73 5f 61 ..Note.that.unlike.`_triangles_a
1d80 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 28 29 60 2c 20 74 68 69 73 20 66 75 6e 63 74 69 6f 6e nd_degree_iter()`,.this.function
1da0 20 63 6f 75 6e 74 73 0a 20 20 20 20 64 69 72 65 63 74 65 64 20 74 72 69 61 6e 67 6c 65 73 20 73 .counts.....directed.triangles.s
1dc0 6f 20 64 6f 65 73 20 6e 6f 74 20 63 6f 75 6e 74 20 74 72 69 61 6e 67 6c 65 73 20 74 77 69 63 65 o.does.not.count.triangles.twice
1de0 2e 0a 0a 20 20 20 20 63 01 00 00 00 00 00 00 00 00 00 00 00 05 00 00 00 33 00 00 00 f3 5c 00 00 .......c................3....\..
1e00 00 95 01 4b 00 01 00 97 00 7c 00 5d 23 00 00 7d 01 7c 01 89 02 6a 00 00 00 00 00 00 00 00 00 00 ...K.....|.]#..}.|...j..........
1e20 00 00 00 00 00 00 00 00 00 7c 01 19 00 00 00 89 02 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 .........|.......j..............
1e40 00 00 00 00 00 7c 01 19 00 00 00 66 03 96 01 97 01 01 00 8c 25 04 00 79 00 ad 03 77 01 72 2b 00 .....|.....f........%..y...w.r+.
1e60 00 00 a9 02 da 05 5f 70 72 65 64 da 05 5f 73 75 63 63 72 2d 00 00 00 73 03 00 00 00 20 20 80 72 ......_pred.._succr-...s.......r
1e80 27 00 00 00 72 2f 00 00 00 7a 36 5f 64 69 72 65 63 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 5f 61 '...r/...z6_directed_triangles_a
1ea0 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 nd_degree_iter.<locals>.<genexpr
1ec0 3e a2 00 00 00 f3 28 00 00 00 f8 e8 00 f8 80 00 d2 11 4c b0 21 90 31 90 61 97 67 91 67 98 61 91 >.....(...........L.!.1.a.g.g.a.
1ee0 6a a0 21 a7 27 a1 27 a8 21 a1 2a d4 12 2d d1 11 4c f9 f3 04 00 00 00 83 29 2c 01 72 02 00 00 00 j.!.'.'.!.*..-..L.......),.r....
1f00 63 01 00 00 00 00 00 00 00 00 00 00 00 02 00 00 00 33 00 00 00 f3 20 00 00 00 4b 00 01 00 97 00 c................3........K.....
1f20 7c 00 5d 06 00 00 7d 01 64 00 96 01 97 01 01 00 8c 08 04 00 79 01 ad 03 77 01 72 44 00 00 00 72 |.]...}.d...........y...w.rD...r
1f40 2c 00 00 00 29 02 72 2e 00 00 00 72 37 00 00 00 73 02 00 00 00 20 20 72 27 00 00 00 72 2f 00 00 ,...).r....r7...s......r'...r/..
1f60 00 7a 36 5f 64 69 72 65 63 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 5f 61 6e 64 5f 64 65 67 72 65 .z6_directed_triangles_and_degre
1f80 65 5f 69 74 65 72 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 3e ac 00 00 00 73 18 00 e_iter.<locals>.<genexpr>....s..
1fa0 00 00 e8 00 f8 80 00 f2 00 08 26 0e e0 14 15 f4 03 00 11 12 f1 03 08 26 0e f9 73 04 00 00 00 82 ..........&............&..s.....
1fc0 0c 0e 01 4e 29 07 72 3a 00 00 00 72 33 00 00 00 72 04 00 00 00 72 69 00 00 00 72 6a 00 00 00 72 ...N).r:...r3...r....ri...rj...r
1fe0 3b 00 00 00 72 16 00 00 00 29 0e 72 18 00 00 00 72 19 00 00 00 72 3c 00 00 00 72 5d 00 00 00 da ;...r....).r....r....r<...r]....
2000 05 70 72 65 64 73 da 05 73 75 63 63 73 da 06 69 70 72 65 64 73 da 06 69 73 75 63 63 73 da 12 64 .preds..succs..ipreds..isuccs..d
2020 69 72 65 63 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 72 62 00 00 00 da 06 6a 70 72 65 64 73 da 06 irected_trianglesrb.....jpreds..
2040 6a 73 75 63 63 73 da 06 64 74 6f 74 61 6c da 0e 64 62 69 64 69 72 65 63 74 69 6f 6e 61 6c 73 0e jsuccs..dtotal..dbidirectionals.
2060 00 00 00 60 20 20 20 20 20 20 20 20 20 20 20 20 20 72 27 00 00 00 da 23 5f 64 69 72 65 63 74 65 ...`.............r'....#_directe
2080 64 5f 74 72 69 61 6e 67 6c 65 73 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 72 77 00 00 00 d_triangles_and_degree_iterrw...
20a0 98 00 00 00 73 10 01 00 00 f8 e8 00 f8 80 00 f3 14 00 12 4d 01 b0 71 b7 7d b1 7d c0 55 d3 37 4b ....s..............M..q.}.}.U.7K
20c0 d4 11 4c 80 4a e0 1b 25 f2 00 13 05 3e 89 0f 88 01 88 35 90 25 dc 11 14 90 55 93 1a 98 71 98 63 ..L.J..%....>.....5.%....U...q.c
20e0 d1 11 21 88 06 dc 11 14 90 55 93 1a 98 71 98 63 d1 11 21 88 06 e0 1d 1e d0 08 1a dc 11 16 90 76 ..!......U...q.c..!............v
2100 98 76 d3 11 26 f2 00 0b 09 0e 88 41 dc 15 18 98 11 9f 17 99 17 a0 11 99 1a 93 5f a8 01 a0 73 d1 .v..&......A.............._...s.
2120 15 2a 88 46 dc 15 18 98 11 9f 17 99 17 a0 11 99 1a 93 5f a8 01 a0 73 d1 15 2a 88 46 d8 0c 1e a4 .*.F.............._...s..*.F....
2140 23 f1 00 08 26 0e e4 19 1e d8 15 1b 98 66 91 5f d8 15 1b 98 66 91 5f d8 15 1b 98 66 91 5f d8 15 #...&........f._....f._....f._..
2160 1b 98 66 91 5f f3 09 05 1a 12 f4 05 08 26 0e f3 00 08 23 0e f1 00 08 0d 0e d1 0c 1e f0 07 0b 09 ..f._........&....#.............
2180 0e f4 18 00 12 15 90 56 93 1b 9c 73 a0 36 9b 7b d1 11 2a 88 06 dc 19 1c 98 56 a0 66 99 5f d3 19 .......V...s.6.{..*......V.f._..
21a0 2d 88 0e d8 0f 10 90 26 98 2e d0 2a 3c d0 0e 3d d3 08 3d f1 27 13 05 3e f9 73 06 00 00 00 83 43 -......&...*<..=..=.'..>.s.....C
21c0 2a 43 2d 01 63 03 00 00 00 00 00 00 00 00 00 00 00 0d 00 00 00 23 00 00 00 f3 ce 07 00 00 87 00 *C-.c................#..........
21e0 87 02 87 12 4b 00 01 00 97 00 64 01 64 02 6c 00 7d 03 89 02 81 13 89 00 6a 03 00 00 00 00 00 00 ....K.....d.d.l.}.......j.......
2200 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 64 01 6b 28 00 00 72 03 64 03 8a 12 ....................d.k(..r.d...
2220 6e 24 74 05 00 00 00 00 00 00 00 00 88 02 66 01 64 04 84 08 89 00 6a 07 00 00 00 00 00 00 00 00 n$t...........f.d.....j.........
2240 00 00 00 00 00 00 00 00 00 00 64 05 ac 06 ab 01 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 ..........d...........D.........
2260 ab 01 00 00 00 00 00 00 8a 12 88 00 66 01 64 07 84 08 89 00 6a 09 00 00 00 00 00 00 00 00 00 00 ............f.d.....j...........
2280 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 7d 04 88 00 ........|.........D.........}...
22a0 88 12 88 02 66 03 64 08 84 08 7d 05 7c 04 44 00 90 03 5d 4f 00 00 5c 03 00 00 7d 06 7d 07 7d 08 ....f.d...}.|.D...]O..\...}.}.}.
22c0 74 0b 00 00 00 00 00 00 00 00 7c 07 ab 01 00 00 00 00 00 00 7c 06 68 01 7a 0a 00 00 7d 09 74 0b t.........|.........|.h.z...}.t.
22e0 00 00 00 00 00 00 00 00 7c 08 ab 01 00 00 00 00 00 00 7c 06 68 01 7a 0a 00 00 7d 0a 64 01 7d 0b ........|.........|.h.z...}.d.}.
2300 7c 09 44 00 90 01 5d 73 00 00 7d 0c 74 0b 00 00 00 00 00 00 00 00 89 00 6a 0c 00 00 00 00 00 00 |.D...]s..}.t...........j.......
2320 00 00 00 00 00 00 00 00 00 00 00 00 7c 0c 19 00 00 00 ab 01 00 00 00 00 00 00 7c 0c 68 01 7a 0a ............|.............|.h.z.
2340 00 00 7d 0d 74 0b 00 00 00 00 00 00 00 00 89 00 6a 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ..}.t...........j...............
2360 00 00 00 00 7c 0c 19 00 00 00 ab 01 00 00 00 00 00 00 7c 0c 68 01 7a 0a 00 00 7d 0e 7c 0b 7c 03 ....|.............|.h.z...}.|.|.
2380 6a 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 09 7c 0d 7a 01 00 00 44 00 8f 0f j...................|.|.z...D...
23a0 63 02 67 00 63 02 5d 1f 00 00 7d 0f 02 00 7c 05 7c 0c 7c 06 ab 02 00 00 00 00 00 00 02 00 7c 05 c.g.c.]...}...|.|.|...........|.
23c0 7c 0f 7c 06 ab 02 00 00 00 00 00 00 7a 05 00 00 02 00 7c 05 7c 0f 7c 0c ab 02 00 00 00 00 00 00 |.|.........z.....|.|.|.........
23e0 7a 05 00 00 91 02 8c 21 04 00 63 02 7d 0f ab 01 00 00 00 00 00 00 6a 13 00 00 00 00 00 00 00 00 z......!..c.}.........j.........
2400 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 7a 0d 00 00 7d 0b 7c 0b 7c 03 6a 11 00 00 ..................z...}.|.|.j...
2420 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 09 7c 0e 7a 01 00 00 44 00 8f 0f 63 02 67 00 ................|.|.z...D...c.g.
2440 63 02 5d 1f 00 00 7d 0f 02 00 7c 05 7c 0c 7c 06 ab 02 00 00 00 00 00 00 02 00 7c 05 7c 0f 7c 06 c.]...}...|.|.|...........|.|.|.
2460 ab 02 00 00 00 00 00 00 7a 05 00 00 02 00 7c 05 7c 0c 7c 0f ab 02 00 00 00 00 00 00 7a 05 00 00 ........z.....|.|.|.........z...
2480 91 02 8c 21 04 00 63 02 7d 0f ab 01 00 00 00 00 00 00 6a 13 00 00 00 00 00 00 00 00 00 00 00 00 ...!..c.}.........j.............
24a0 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 7a 0d 00 00 7d 0b 7c 0b 7c 03 6a 11 00 00 00 00 00 00 ..............z...}.|.|.j.......
24c0 00 00 00 00 00 00 00 00 00 00 00 00 7c 0a 7c 0d 7a 01 00 00 44 00 8f 0f 63 02 67 00 63 02 5d 1f ............|.|.z...D...c.g.c.].
24e0 00 00 7d 0f 02 00 7c 05 7c 0c 7c 06 ab 02 00 00 00 00 00 00 02 00 7c 05 7c 06 7c 0f ab 02 00 00 ..}...|.|.|...........|.|.|.....
2500 00 00 00 00 7a 05 00 00 02 00 7c 05 7c 0f 7c 0c ab 02 00 00 00 00 00 00 7a 05 00 00 91 02 8c 21 ....z.....|.|.|.........z......!
2520 04 00 63 02 7d 0f ab 01 00 00 00 00 00 00 6a 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ..c.}.........j.................
2540 00 00 ab 00 00 00 00 00 00 00 7a 0d 00 00 7d 0b 7c 0b 7c 03 6a 11 00 00 00 00 00 00 00 00 00 00 ..........z...}.|.|.j...........
2560 00 00 00 00 00 00 00 00 7c 0a 7c 0e 7a 01 00 00 44 00 8f 0f 63 02 67 00 63 02 5d 1f 00 00 7d 0f ........|.|.z...D...c.g.c.]...}.
2580 02 00 7c 05 7c 0c 7c 06 ab 02 00 00 00 00 00 00 02 00 7c 05 7c 06 7c 0f ab 02 00 00 00 00 00 00 ..|.|.|...........|.|.|.........
25a0 7a 05 00 00 02 00 7c 05 7c 0c 7c 0f ab 02 00 00 00 00 00 00 7a 05 00 00 91 02 8c 21 04 00 63 02 z.....|.|.|.........z......!..c.
25c0 7d 0f ab 01 00 00 00 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 }.........j.....................
25e0 00 00 00 00 00 00 7a 0d 00 00 7d 0b 90 01 8c 76 04 00 7c 0a 44 00 90 01 5d 73 00 00 7d 0c 74 0b ......z...}....v..|.D...]s..}.t.
2600 00 00 00 00 00 00 00 00 89 00 6a 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0c ..........j...................|.
2620 19 00 00 00 ab 01 00 00 00 00 00 00 7c 0c 68 01 7a 0a 00 00 7d 0d 74 0b 00 00 00 00 00 00 00 00 ............|.h.z...}.t.........
2640 89 00 6a 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0c 19 00 00 00 ab 01 00 00 ..j...................|.........
2660 00 00 00 00 7c 0c 68 01 7a 0a 00 00 7d 0e 7c 0b 7c 03 6a 11 00 00 00 00 00 00 00 00 00 00 00 00 ....|.h.z...}.|.|.j.............
2680 00 00 00 00 00 00 7c 09 7c 0d 7a 01 00 00 44 00 8f 0f 63 02 67 00 63 02 5d 1f 00 00 7d 0f 02 00 ......|.|.z...D...c.g.c.]...}...
26a0 7c 05 7c 06 7c 0c ab 02 00 00 00 00 00 00 02 00 7c 05 7c 0f 7c 06 ab 02 00 00 00 00 00 00 7a 05 |.|.|...........|.|.|.........z.
26c0 00 00 02 00 7c 05 7c 0f 7c 0c ab 02 00 00 00 00 00 00 7a 05 00 00 91 02 8c 21 04 00 63 02 7d 0f ....|.|.|.........z......!..c.}.
26e0 ab 01 00 00 00 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 ........j.......................
2700 00 00 00 00 7a 0d 00 00 7d 0b 7c 0b 7c 03 6a 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ....z...}.|.|.j.................
2720 00 00 7c 09 7c 0e 7a 01 00 00 44 00 8f 0f 63 02 67 00 63 02 5d 1f 00 00 7d 0f 02 00 7c 05 7c 06 ..|.|.z...D...c.g.c.]...}...|.|.
2740 7c 0c ab 02 00 00 00 00 00 00 02 00 7c 05 7c 0f 7c 06 ab 02 00 00 00 00 00 00 7a 05 00 00 02 00 |...........|.|.|.........z.....
2760 7c 05 7c 0c 7c 0f ab 02 00 00 00 00 00 00 7a 05 00 00 91 02 8c 21 04 00 63 02 7d 0f ab 01 00 00 |.|.|.........z......!..c.}.....
2780 00 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...........................
27a0 7a 0d 00 00 7d 0b 7c 0b 7c 03 6a 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0a z...}.|.|.j...................|.
27c0 7c 0d 7a 01 00 00 44 00 8f 0f 63 02 67 00 63 02 5d 1f 00 00 7d 0f 02 00 7c 05 7c 06 7c 0c ab 02 |.z...D...c.g.c.]...}...|.|.|...
27e0 00 00 00 00 00 00 02 00 7c 05 7c 06 7c 0f ab 02 00 00 00 00 00 00 7a 05 00 00 02 00 7c 05 7c 0f ........|.|.|.........z.....|.|.
2800 7c 0c ab 02 00 00 00 00 00 00 7a 05 00 00 91 02 8c 21 04 00 63 02 7d 0f ab 01 00 00 00 00 00 00 |.........z......!..c.}.........
2820 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 7a 0d 00 00 j...........................z...
2840 7d 0b 7c 0b 7c 03 6a 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0a 7c 0e 7a 01 }.|.|.j...................|.|.z.
2860 00 00 44 00 8f 0f 63 02 67 00 63 02 5d 1f 00 00 7d 0f 02 00 7c 05 7c 06 7c 0c ab 02 00 00 00 00 ..D...c.g.c.]...}...|.|.|.......
2880 00 00 02 00 7c 05 7c 06 7c 0f ab 02 00 00 00 00 00 00 7a 05 00 00 02 00 7c 05 7c 0c 7c 0f ab 02 ....|.|.|.........z.....|.|.|...
28a0 00 00 00 00 00 00 7a 05 00 00 91 02 8c 21 04 00 63 02 7d 0f ab 01 00 00 00 00 00 00 6a 13 00 00 ......z......!..c.}.........j...
28c0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 7a 0d 00 00 7d 0b 90 01 ........................z...}...
28e0 8c 76 04 00 74 15 00 00 00 00 00 00 00 00 7c 09 ab 01 00 00 00 00 00 00 74 15 00 00 00 00 00 00 .v..t.........|.........t.......
2900 00 00 7c 0a ab 01 00 00 00 00 00 00 7a 00 00 00 7d 10 74 15 00 00 00 00 00 00 00 00 7c 09 7c 0a ..|.........z...}.t.........|.|.
2920 7a 01 00 00 ab 01 00 00 00 00 00 00 7d 11 7c 06 7c 10 7c 11 74 17 00 00 00 00 00 00 00 00 7c 0b z...........}.|.|.|.t.........|.
2940 ab 01 00 00 00 00 00 00 66 04 96 01 97 01 01 00 90 03 8c 52 04 00 79 02 63 02 01 00 63 02 7d 0f ........f..........R..y.c...c.}.
2960 77 00 63 02 01 00 63 02 7d 0f 77 00 63 02 01 00 63 02 7d 0f 77 00 63 02 01 00 63 02 7d 0f 77 00 w.c...c.}.w.c...c.}.w.c...c.}.w.
2980 63 02 01 00 63 02 7d 0f 77 00 63 02 01 00 63 02 7d 0f 77 00 63 02 01 00 63 02 7d 0f 77 00 63 02 c...c.}.w.c...c.}.w.c...c.}.w.c.
29a0 01 00 63 02 7d 0f 77 00 ad 03 77 01 29 09 61 1e 01 00 00 52 65 74 75 72 6e 20 61 6e 20 69 74 65 ..c.}.w...w.).a....Return.an.ite
29c0 72 61 74 6f 72 20 6f 66 0a 20 20 20 20 28 6e 6f 64 65 2c 20 74 6f 74 61 6c 5f 64 65 67 72 65 65 rator.of.....(node,.total_degree
29e0 2c 20 72 65 63 69 70 72 6f 63 61 6c 5f 64 65 67 72 65 65 2c 20 64 69 72 65 63 74 65 64 5f 77 65 ,.reciprocal_degree,.directed_we
2a00 69 67 68 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 29 2e 0a 0a 20 20 20 20 55 73 65 64 20 66 6f 72 ighted_triangles).......Used.for
2a20 20 64 69 72 65 63 74 65 64 20 77 65 69 67 68 74 65 64 20 63 6c 75 73 74 65 72 69 6e 67 2e 0a 20 .directed.weighted.clustering...
2a40 20 20 20 4e 6f 74 65 20 74 68 61 74 20 75 6e 6c 69 6b 65 20 60 5f 77 65 69 67 68 74 65 64 5f 74 ...Note.that.unlike.`_weighted_t
2a60 72 69 61 6e 67 6c 65 73 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 28 29 60 2c 20 74 68 69 riangles_and_degree_iter()`,.thi
2a80 73 20 66 75 6e 63 74 69 6f 6e 20 63 6f 75 6e 74 73 0a 20 20 20 20 64 69 72 65 63 74 65 64 20 74 s.function.counts.....directed.t
2aa0 72 69 61 6e 67 6c 65 73 20 73 6f 20 64 6f 65 73 20 6e 6f 74 20 63 6f 75 6e 74 20 74 72 69 61 6e riangles.so.does.not.count.trian
2ac0 67 6c 65 73 20 74 77 69 63 65 2e 0a 0a 20 20 20 20 72 02 00 00 00 4e 72 42 00 00 00 63 01 00 00 gles.twice.......r....NrB...c...
2ae0 00 00 00 00 00 00 00 00 00 05 00 00 00 33 00 00 00 f3 4a 00 00 00 95 01 4b 00 01 00 97 00 7c 00 .............3....J.....K.....|.
2b00 5d 1a 00 00 5c 03 00 00 7d 01 7d 02 7d 03 7c 03 6a 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ]...\...}.}.}.|.j...............
2b20 00 00 00 00 89 04 64 00 ab 02 00 00 00 00 00 00 96 01 97 01 01 00 8c 1c 04 00 79 01 ad 03 77 01 ......d...................y...w.
2b40 72 44 00 00 00 72 45 00 00 00 72 47 00 00 00 73 05 00 00 00 20 20 20 20 80 72 27 00 00 00 72 2f rD...rE...rG...s.........r'...r/
2b60 00 00 00 7a 3f 5f 64 69 72 65 63 74 65 64 5f 77 65 69 67 68 74 65 64 5f 74 72 69 61 6e 67 6c 65 ...z?_directed_weighted_triangle
2b80 73 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 s_and_degree_iter.<locals>.<gene
2ba0 78 70 72 3e c9 00 00 00 72 49 00 00 00 72 4a 00 00 00 54 72 4b 00 00 00 63 01 00 00 00 00 00 00 xpr>....rI...rJ...TrK...c.......
2bc0 00 00 00 00 00 05 00 00 00 33 00 00 00 f3 5c 00 00 00 95 01 4b 00 01 00 97 00 7c 00 5d 23 00 00 .........3....\.....K.....|.]#..
2be0 7d 01 7c 01 89 02 6a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 01 19 00 00 00 }.|...j...................|.....
2c00 89 02 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 01 19 00 00 00 66 03 96 01 ..j...................|.....f...
2c20 97 01 01 00 8c 25 04 00 79 00 ad 03 77 01 72 2b 00 00 00 72 68 00 00 00 72 2d 00 00 00 73 03 00 .....%..y...w.r+...rh...r-...s..
2c40 00 00 20 20 80 72 27 00 00 00 72 2f 00 00 00 7a 3f 5f 64 69 72 65 63 74 65 64 5f 77 65 69 67 68 .....r'...r/...z?_directed_weigh
2c60 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 74 65 72 2e 3c 6c ted_triangles_and_degree_iter.<l
2c80 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 3e cb 00 00 00 72 6b 00 00 00 72 6c 00 00 00 63 02 ocals>.<genexpr>....rk...rl...c.
2ca0 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 13 00 00 00 f3 3a 00 00 00 95 03 97 00 89 02 7c 00 ....................:.........|.
2cc0 19 00 00 00 7c 01 19 00 00 00 6a 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 89 04 ....|.....j.....................
2ce0 64 01 ab 02 00 00 00 00 00 00 89 03 7a 0b 00 00 53 00 72 4f 00 00 00 72 45 00 00 00 72 50 00 00 d...........z...S.rO...rE...rP..
2d00 00 73 05 00 00 00 20 20 80 80 80 72 27 00 00 00 72 52 00 00 00 7a 38 5f 64 69 72 65 63 74 65 64 .s.........r'...rR...z8_directed
2d20 5f 77 65 69 67 68 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 5f 61 6e 64 5f 64 65 67 72 65 65 5f 69 _weighted_triangles_and_degree_i
2d40 74 65 72 2e 3c 6c 6f 63 61 6c 73 3e 2e 77 74 cd 00 00 00 72 53 00 00 00 72 54 00 00 00 29 0c 72 ter.<locals>.wt....rS...rT...).r
2d60 55 00 00 00 72 56 00 00 00 72 57 00 00 00 72 58 00 00 00 72 3a 00 00 00 72 33 00 00 00 72 69 00 U...rV...rW...rX...r:...r3...ri.
2d80 00 00 72 6a 00 00 00 72 5a 00 00 00 72 3b 00 00 00 72 16 00 00 00 72 5b 00 00 00 29 13 72 18 00 ..rj...rZ...r;...r....r[...).r..
2da0 00 00 72 19 00 00 00 72 40 00 00 00 72 5c 00 00 00 72 3c 00 00 00 72 52 00 00 00 72 5d 00 00 00 ..r....r@...r\...r<...rR...r]...
2dc0 72 6e 00 00 00 72 6f 00 00 00 72 70 00 00 00 72 71 00 00 00 72 72 00 00 00 72 62 00 00 00 72 73 rn...ro...rp...rq...rr...rb...rs
2de0 00 00 00 72 74 00 00 00 72 37 00 00 00 72 75 00 00 00 72 76 00 00 00 72 51 00 00 00 73 13 00 00 ...rt...r7...ru...rv...rQ...s...
2e00 00 60 20 60 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 40 72 27 00 00 00 da 2c 5f 64 69 72 65 .`.`...............@r'....,_dire
2e20 63 74 65 64 5f 77 65 69 67 68 74 65 64 5f 74 72 69 61 6e 67 6c 65 73 5f 61 6e 64 5f 64 65 67 72 cted_weighted_triangles_and_degr
2e40 65 65 5f 69 74 65 72 72 7c 00 00 00 ba 00 00 00 73 e4 03 00 00 fa e8 00 f8 80 00 f3 14 00 05 17 ee_iterr|.......s...............
2e60 e0 07 0d 80 7e 98 11 d7 19 2a d1 19 2a d3 19 2c b0 01 d2 19 31 d8 15 16 89 0a e4 15 18 d3 18 4c ....~....*..*..,....1..........L
2e80 b8 11 bf 17 b9 17 c0 64 b8 17 d3 39 4b d4 18 4c d3 15 4c 88 0a e3 11 4c b0 71 b7 7d b1 7d c0 55 .......d...9K..L..L....L.q.}.}.U
2ea0 d3 37 4b d4 11 4c 80 4a f6 04 01 05 33 f0 06 00 1c 26 f3 00 27 05 45 01 89 0f 88 01 88 35 90 25 .7K..L.J....3....&..'.E......5.%
2ec0 dc 11 14 90 55 93 1a 98 71 98 63 d1 11 21 88 06 dc 11 14 90 55 93 1a 98 71 98 63 d1 11 21 88 06 ....U...q.c..!......U...q.c..!..
2ee0 e0 1d 1e d0 08 1a d8 11 17 f3 00 0e 09 14 88 41 dc 15 18 98 11 9f 17 99 17 a0 11 99 1a 93 5f a8 ...............A.............._.
2f00 01 a0 73 d1 15 2a 88 46 dc 15 18 98 11 9f 17 99 17 a0 11 99 1a 93 5f a8 01 a0 73 d1 15 2a 88 46 ..s..*.F.............._...s..*.F
2f20 d8 0c 1e a0 22 a7 27 a1 27 d8 3b 41 c0 46 b9 3f d6 10 4b b0 61 91 22 90 51 98 01 93 28 99 52 a0 ....".'.'.;A.F.?..K.a.".Q...(.R.
2f40 01 a0 31 9b 58 d1 12 25 a9 02 a8 31 a8 61 ab 08 d3 12 30 d2 10 4b f3 03 02 23 0e e7 0e 11 89 63 ..1.X..%...1.a....0..K...#.....c
2f60 8b 65 f1 05 02 0d 14 d0 0c 1e f0 06 00 0d 1f a0 22 a7 27 a1 27 d8 3b 41 c0 46 b9 3f d6 10 4b b0 .e..............".'.'.;A.F.?..K.
2f80 61 91 22 90 51 98 01 93 28 99 52 a0 01 a0 31 9b 58 d1 12 25 a9 02 a8 31 a8 61 ab 08 d3 12 30 d2 a.".Q...(.R...1.X..%...1.a....0.
2fa0 10 4b f3 03 02 23 0e e7 0e 11 89 63 8b 65 f1 05 02 0d 14 d0 0c 1e f0 06 00 0d 1f a0 22 a7 27 a1 .K...#.....c.e..............".'.
2fc0 27 d8 3b 41 c0 46 b9 3f d6 10 4b b0 61 91 22 90 51 98 01 93 28 99 52 a0 01 a0 31 9b 58 d1 12 25 '.;A.F.?..K.a.".Q...(.R...1.X..%
2fe0 a9 02 a8 31 a8 61 ab 08 d3 12 30 d2 10 4b f3 03 02 23 0e e7 0e 11 89 63 8b 65 f1 05 02 0d 14 d0 ...1.a....0..K...#.....c.e......
3000 0c 1e f0 06 00 0d 1f a0 22 a7 27 a1 27 d8 3b 41 c0 46 b9 3f d6 10 4b b0 61 91 22 90 51 98 01 93 ........".'.'.;A.F.?..K.a.".Q...
3020 28 99 52 a0 01 a0 31 9b 58 d1 12 25 a9 02 a8 31 a8 61 ab 08 d3 12 30 d2 10 4b f3 03 02 23 0e e7 (.R...1.X..%...1.a....0..K...#..
3040 0e 11 89 63 8b 65 f1 05 02 0d 14 d2 0c 1e f0 19 0e 09 14 f0 20 00 12 18 f3 00 0e 09 14 88 41 dc ...c.e........................A.
3060 15 18 98 11 9f 17 99 17 a0 11 99 1a 93 5f a8 01 a0 73 d1 15 2a 88 46 dc 15 18 98 11 9f 17 99 17 ............._...s..*.F.........
3080 a0 11 99 1a 93 5f a8 01 a0 73 d1 15 2a 88 46 d8 0c 1e a0 22 a7 27 a1 27 d8 3b 41 c0 46 b9 3f d6 ....._...s..*.F....".'.'.;A.F.?.
30a0 10 4b b0 61 91 22 90 51 98 01 93 28 99 52 a0 01 a0 31 9b 58 d1 12 25 a9 02 a8 31 a8 61 ab 08 d3 .K.a.".Q...(.R...1.X..%...1.a...
30c0 12 30 d2 10 4b f3 03 02 23 0e e7 0e 11 89 63 8b 65 f1 05 02 0d 14 d0 0c 1e f0 06 00 0d 1f a0 22 .0..K...#.....c.e.............."
30e0 a7 27 a1 27 d8 3b 41 c0 46 b9 3f d6 10 4b b0 61 91 22 90 51 98 01 93 28 99 52 a0 01 a0 31 9b 58 .'.'.;A.F.?..K.a.".Q...(.R...1.X
3100 d1 12 25 a9 02 a8 31 a8 61 ab 08 d3 12 30 d2 10 4b f3 03 02 23 0e e7 0e 11 89 63 8b 65 f1 05 02 ..%...1.a....0..K...#.....c.e...
3120 0d 14 d0 0c 1e f0 06 00 0d 1f a0 22 a7 27 a1 27 d8 3b 41 c0 46 b9 3f d6 10 4b b0 61 91 22 90 51 ...........".'.'.;A.F.?..K.a.".Q
3140 98 01 93 28 99 52 a0 01 a0 31 9b 58 d1 12 25 a9 02 a8 31 a8 61 ab 08 d3 12 30 d2 10 4b f3 03 02 ...(.R...1.X..%...1.a....0..K...
3160 23 0e e7 0e 11 89 63 8b 65 f1 05 02 0d 14 d0 0c 1e f0 06 00 0d 1f a0 22 a7 27 a1 27 d8 3b 41 c0 #.....c.e..............".'.'.;A.
3180 46 b9 3f d6 10 4b b0 61 91 22 90 51 98 01 93 28 99 52 a0 01 a0 31 9b 58 d1 12 25 a9 02 a8 31 a8 F.?..K.a.".Q...(.R...1.X..%...1.
31a0 61 ab 08 d3 12 30 d2 10 4b f3 03 02 23 0e e7 0e 11 89 63 8b 65 f1 05 02 0d 14 d2 0c 1e f0 19 0e a....0..K...#.....c.e...........
31c0 09 14 f4 20 00 12 15 90 56 93 1b 9c 73 a0 36 9b 7b d1 11 2a 88 06 dc 19 1c 98 56 a0 66 99 5f d3 ........V...s.6.{..*......V.f._.
31e0 19 2d 88 0e d8 0f 10 90 26 98 2e ac 25 d0 30 42 d3 2a 43 d0 0e 44 d4 08 44 f1 4f 01 27 05 45 01 .-......&...%.0B.*C..D..D.O.'.E.
3200 f9 f2 12 00 11 4c 01 f9 f2 06 00 11 4c 01 f9 f2 06 00 11 4c 01 f9 f2 06 00 11 4c 01 f9 f2 0e 00 .....L......L......L......L.....
3220 11 4c 01 f9 f2 06 00 11 4c 01 f9 f2 06 00 11 4c 01 f9 f2 06 00 11 4c 01 f9 73 68 00 00 00 85 43 .L......L......L......L..sh....C
3240 1d 4f 25 01 c3 22 24 4e 3d 0e c4 06 2a 4f 25 01 c4 30 24 4f 02 0e c5 14 2a 4f 25 01 c5 3e 24 4f .O%.."$N=...*O%..0$O....*O%..>$O
3260 07 0e c6 22 2a 4f 25 01 c7 0c 24 4f 0c 0e c7 30 41 2b 4f 25 01 c9 1b 24 4f 11 0e c9 3f 2a 4f 25 ..."*O%...$O...0A+O%...$O...?*O%
3280 01 ca 29 24 4f 16 0e cb 0d 2a 4f 25 01 cb 37 24 4f 1b 0e cc 1b 2a 4f 25 01 cd 05 24 4f 20 0e cd ..)$O....*O%..7$O....*O%...$O...
32a0 29 41 3c 4f 25 01 29 01 da 0a 65 64 67 65 5f 61 74 74 72 73 63 04 00 00 00 00 00 00 00 00 00 00 )A<O%.)...edge_attrsc...........
32c0 00 06 00 00 00 03 00 00 00 f3 b2 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 7c 00 7c 01 7c 02 ................t.........|.|.|.
32e0 ac 01 ab 03 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 ab 00 ..........j.....................
3300 00 00 00 00 00 00 7d 04 7c 03 73 1e 7c 04 44 00 8f 05 63 02 67 00 63 02 5d 13 00 00 7d 05 74 05 ......}.|.s.|.D...c.g.c.]...}.t.
3320 00 00 00 00 00 00 00 00 7c 05 ab 01 00 00 00 00 00 00 64 02 6b 44 00 00 73 01 8c 12 7c 05 91 02 ........|.........d.kD..s...|...
3340 8c 15 04 00 7d 04 7d 05 74 07 00 00 00 00 00 00 00 00 7c 04 ab 01 00 00 00 00 00 00 74 09 00 00 ....}.}.t.........|.........t...
3360 00 00 00 00 00 00 7c 04 ab 01 00 00 00 00 00 00 7a 0b 00 00 53 00 63 02 01 00 63 02 7d 05 77 00 ......|.........z...S.c...c.}.w.
3380 29 03 75 ef 05 00 00 43 6f 6d 70 75 74 65 20 74 68 65 20 61 76 65 72 61 67 65 20 63 6c 75 73 74 ).u....Compute.the.average.clust
33a0 65 72 69 6e 67 20 63 6f 65 66 66 69 63 69 65 6e 74 20 66 6f 72 20 74 68 65 20 67 72 61 70 68 20 ering.coefficient.for.the.graph.
33c0 47 2e 0a 0a 20 20 20 20 54 68 65 20 63 6c 75 73 74 65 72 69 6e 67 20 63 6f 65 66 66 69 63 69 65 G.......The.clustering.coefficie
33e0 6e 74 20 66 6f 72 20 74 68 65 20 67 72 61 70 68 20 69 73 20 74 68 65 20 61 76 65 72 61 67 65 2c nt.for.the.graph.is.the.average,
3400 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 0a 0a 20 20 20 20 20 20 20 43 20 3d 20 5c 66 72 61 .........math::.........C.=.\fra
3420 63 7b 31 7d 7b 6e 7d 5c 73 75 6d 5f 7b 76 20 5c 69 6e 20 47 7d 20 63 5f 76 2c 0a 0a 20 20 20 20 c{1}{n}\sum_{v.\in.G}.c_v,......
3440 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 6e 60 20 69 73 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 where.:math:`n`.is.the.number.of
3460 20 6e 6f 64 65 73 20 69 6e 20 60 47 60 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 .nodes.in.`G`.......Parameters..
3480 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 0a 0a 20 20 20 ...----------.....G.:.graph.....
34a0 20 6e 6f 64 65 73 20 3a 20 63 6f 6e 74 61 69 6e 65 72 20 6f 66 20 6e 6f 64 65 73 2c 20 6f 70 74 .nodes.:.container.of.nodes,.opt
34c0 69 6f 6e 61 6c 20 28 64 65 66 61 75 6c 74 3d 61 6c 6c 20 6e 6f 64 65 73 20 69 6e 20 47 29 0a 20 ional.(default=all.nodes.in.G)..
34e0 20 20 20 20 20 20 43 6f 6d 70 75 74 65 20 61 76 65 72 61 67 65 20 63 6c 75 73 74 65 72 69 6e 67 ......Compute.average.clustering
3500 20 66 6f 72 20 6e 6f 64 65 73 20 69 6e 20 74 68 69 73 20 63 6f 6e 74 61 69 6e 65 72 2e 0a 0a 20 .for.nodes.in.this.container....
3520 20 20 20 77 65 69 67 68 74 20 3a 20 73 74 72 69 6e 67 20 6f 72 20 4e 6f 6e 65 2c 20 6f 70 74 69 ...weight.:.string.or.None,.opti
3540 6f 6e 61 6c 20 28 64 65 66 61 75 6c 74 3d 4e 6f 6e 65 29 0a 20 20 20 20 20 20 20 54 68 65 20 65 onal.(default=None)........The.e
3560 64 67 65 20 61 74 74 72 69 62 75 74 65 20 74 68 61 74 20 68 6f 6c 64 73 20 74 68 65 20 6e 75 6d dge.attribute.that.holds.the.num
3580 65 72 69 63 61 6c 20 76 61 6c 75 65 20 75 73 65 64 20 61 73 20 61 20 77 65 69 67 68 74 2e 0a 20 erical.value.used.as.a.weight...
35a0 20 20 20 20 20 20 49 66 20 4e 6f 6e 65 2c 20 74 68 65 6e 20 65 61 63 68 20 65 64 67 65 20 68 61 ......If.None,.then.each.edge.ha
35c0 73 20 77 65 69 67 68 74 20 31 2e 0a 0a 20 20 20 20 63 6f 75 6e 74 5f 7a 65 72 6f 73 20 3a 20 62 s.weight.1.......count_zeros.:.b
35e0 6f 6f 6c 0a 20 20 20 20 20 20 20 49 66 20 46 61 6c 73 65 20 69 6e 63 6c 75 64 65 20 6f 6e 6c 79 ool........If.False.include.only
3600 20 74 68 65 20 6e 6f 64 65 73 20 77 69 74 68 20 6e 6f 6e 7a 65 72 6f 20 63 6c 75 73 74 65 72 69 .the.nodes.with.nonzero.clusteri
3620 6e 67 20 69 6e 20 74 68 65 20 61 76 65 72 61 67 65 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a ng.in.the.average.......Returns.
3640 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 61 76 67 20 3a 20 66 6c 6f 61 74 0a 20 20 20 20 ....-------.....avg.:.float.....
3660 20 20 20 41 76 65 72 61 67 65 20 63 6c 75 73 74 65 72 69 6e 67 0a 0a 20 20 20 20 45 78 61 6d 70 ...Average.clustering......Examp
3680 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 47 20 3d 20 6e 78 2e les.....--------.....>>>.G.=.nx.
36a0 63 6f 6d 70 6c 65 74 65 5f 67 72 61 70 68 28 35 29 0a 20 20 20 20 3e 3e 3e 20 70 72 69 6e 74 28 complete_graph(5).....>>>.print(
36c0 6e 78 2e 61 76 65 72 61 67 65 5f 63 6c 75 73 74 65 72 69 6e 67 28 47 29 29 0a 20 20 20 20 31 2e nx.average_clustering(G)).....1.
36e0 30 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 54 68 69 73 20 0......Notes.....-----.....This.
3700 69 73 20 61 20 73 70 61 63 65 20 73 61 76 69 6e 67 20 72 6f 75 74 69 6e 65 3b 20 69 74 20 6d 69 is.a.space.saving.routine;.it.mi
3720 67 68 74 20 62 65 20 66 61 73 74 65 72 0a 20 20 20 20 74 6f 20 75 73 65 20 74 68 65 20 63 6c 75 ght.be.faster.....to.use.the.clu
3740 73 74 65 72 69 6e 67 20 66 75 6e 63 74 69 6f 6e 20 74 6f 20 67 65 74 20 61 20 6c 69 73 74 20 61 stering.function.to.get.a.list.a
3760 6e 64 20 74 68 65 6e 20 74 61 6b 65 20 74 68 65 20 61 76 65 72 61 67 65 2e 0a 0a 20 20 20 20 53 nd.then.take.the.average.......S
3780 65 6c 66 20 6c 6f 6f 70 73 20 61 72 65 20 69 67 6e 6f 72 65 64 2e 0a 0a 20 20 20 20 52 65 66 65 elf.loops.are.ignored.......Refe
37a0 72 65 6e 63 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 rences.....----------........[1]
37c0 20 47 65 6e 65 72 61 6c 69 7a 61 74 69 6f 6e 73 20 6f 66 20 74 68 65 20 63 6c 75 73 74 65 72 69 .Generalizations.of.the.clusteri
37e0 6e 67 20 63 6f 65 66 66 69 63 69 65 6e 74 20 74 6f 20 77 65 69 67 68 74 65 64 0a 20 20 20 20 20 ng.coefficient.to.weighted......
3800 20 20 63 6f 6d 70 6c 65 78 20 6e 65 74 77 6f 72 6b 73 20 62 79 20 4a 2e 20 53 61 72 61 6d c3 a4 ..complex.networks.by.J..Saram..
3820 6b 69 2c 20 4d 2e 20 4b 69 76 65 6c c3 a4 2c 20 4a 2e 2d 50 2e 20 4f 6e 6e 65 6c 61 2c 0a 20 20 ki,.M..Kivel..,.J.-P..Onnela,...
3840 20 20 20 20 20 4b 2e 20 4b 61 73 6b 69 2c 20 61 6e 64 20 4a 2e 20 4b 65 72 74 c3 a9 73 7a 2c 20 .....K..Kaski,.and.J..Kert..sz,.
3860 50 68 79 73 69 63 61 6c 20 52 65 76 69 65 77 20 45 2c 20 37 35 20 30 32 37 31 30 35 20 28 32 30 Physical.Review.E,.75.027105.(20
3880 30 37 29 2e 0a 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6a 70 6f 6e 6e 65 6c 61 2e 63 6f 6d 2f 07).........http://jponnela.com/
38a0 77 65 62 5f 64 6f 63 75 6d 65 6e 74 73 2f 61 39 2e 70 64 66 0a 20 20 20 20 2e 2e 20 5b 32 5d 20 web_documents/a9.pdf........[2].
38c0 4d 61 72 63 75 73 20 4b 61 69 73 65 72 2c 20 20 4d 65 61 6e 20 63 6c 75 73 74 65 72 69 6e 67 20 Marcus.Kaiser,..Mean.clustering.
38e0 63 6f 65 66 66 69 63 69 65 6e 74 73 3a 20 74 68 65 20 72 6f 6c 65 20 6f 66 20 69 73 6f 6c 61 74 coefficients:.the.role.of.isolat
3900 65 64 0a 20 20 20 20 20 20 20 6e 6f 64 65 73 20 61 6e 64 20 6c 65 61 66 73 20 6f 6e 20 63 6c 75 ed........nodes.and.leafs.on.clu
3920 73 74 65 72 69 6e 67 20 6d 65 61 73 75 72 65 73 20 66 6f 72 20 73 6d 61 6c 6c 2d 77 6f 72 6c 64 stering.measures.for.small-world
3940 20 6e 65 74 77 6f 72 6b 73 2e 0a 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 61 72 78 69 76 2e .networks.........https://arxiv.
3960 6f 72 67 2f 61 62 73 2f 30 38 30 32 2e 32 35 31 32 0a 20 20 20 20 29 01 72 40 00 00 00 72 02 00 org/abs/0802.2512.....).r@...r..
3980 00 00 29 05 72 09 00 00 00 da 06 76 61 6c 75 65 73 da 03 61 62 73 72 3b 00 00 00 72 16 00 00 00 ..).r......values..absr;...r....
39a0 29 06 72 18 00 00 00 72 19 00 00 00 72 40 00 00 00 da 0b 63 6f 75 6e 74 5f 7a 65 72 6f 73 da 01 ).r....r....r@.....count_zeros..
39c0 63 72 1a 00 00 00 73 06 00 00 00 20 20 20 20 20 20 72 27 00 00 00 72 08 00 00 00 72 08 00 00 00 cr....s..........r'...r....r....
39e0 fa 00 00 00 73 53 00 00 00 80 00 f4 6c 01 00 09 13 90 31 90 65 a0 46 d4 08 2b d7 08 32 d1 08 32 ....sS......l.....1.e.F..+..2..2
3a00 d3 08 34 80 41 d9 0b 16 d8 18 19 d6 0c 28 90 31 9c 53 a0 11 9b 56 a0 61 9b 5a 8a 51 d0 0c 28 88 ..4.A........(.1.S...V.a.Z.Q..(.
3a20 01 d0 0c 28 dc 0b 0e 88 71 8b 36 94 43 98 01 93 46 89 3f d0 04 1a f9 f2 03 00 0d 29 73 0a 00 00 ...(....q.6.C...F.?........)s...
3a40 00 a3 13 41 14 04 b7 04 41 14 04 63 03 00 00 00 00 00 00 00 00 00 00 00 0b 00 00 00 03 00 00 00 ...A....A..c....................
3a60 f3 5e 02 00 00 97 00 7c 00 6a 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 .^.....|.j......................
3a80 00 00 00 00 00 72 85 7c 02 81 42 74 03 00 00 00 00 00 00 00 00 7c 00 7c 01 7c 02 ab 03 00 00 00 .....r.|..Bt.........|.|.|......
3aa0 00 00 00 7d 03 7c 03 44 00 8f 04 8f 05 8f 06 8f 07 63 05 69 00 63 02 5d 23 00 00 5c 04 00 00 7d ...}.|.D.........c.i.c.]#..\...}
3ac0 04 7d 05 7d 06 7d 07 7c 04 7c 07 64 01 6b 28 00 00 72 02 64 01 6e 13 7c 07 7c 05 7c 05 64 02 7a .}.}.}.|.|.d.k(..r.d.n.|.|.|.d.z
3ae0 0a 00 00 7a 05 00 00 64 03 7c 06 7a 05 00 00 7a 0a 00 00 64 03 7a 05 00 00 7a 0b 00 00 93 02 8c ...z...d.|.z...z...d.z...z......
3b00 25 04 00 7d 08 7d 06 7d 05 7d 04 7d 07 6e b0 74 05 00 00 00 00 00 00 00 00 7c 00 7c 01 ab 02 00 %..}.}.}.}.}.n.t.........|.|....
3b20 00 00 00 00 00 7d 03 7c 03 44 00 8f 04 8f 05 8f 06 8f 07 63 05 69 00 63 02 5d 23 00 00 5c 04 00 .....}.|.D.........c.i.c.]#..\..
3b40 00 7d 04 7d 05 7d 06 7d 07 7c 04 7c 07 64 01 6b 28 00 00 72 02 64 01 6e 13 7c 07 7c 05 7c 05 64 .}.}.}.}.|.|.d.k(..r.d.n.|.|.|.d
3b60 02 7a 0a 00 00 7a 05 00 00 64 03 7c 06 7a 05 00 00 7a 0a 00 00 64 03 7a 05 00 00 7a 0b 00 00 93 .z...z...d.|.z...z...d.z...z....
3b80 02 8c 25 04 00 7d 08 7d 06 7d 05 7d 04 7d 07 6e 6f 7c 02 81 36 74 07 00 00 00 00 00 00 00 00 7c ..%..}.}.}.}.}.no|..6t.........|
3ba0 00 7c 01 7c 02 ab 03 00 00 00 00 00 00 7d 03 7c 03 44 00 8f 04 8f 09 8f 07 63 04 69 00 63 02 5d .|.|.........}.|.D.......c.i.c.]
3bc0 19 00 00 5c 03 00 00 7d 04 7d 09 7d 07 7c 04 7c 07 64 01 6b 28 00 00 72 02 64 01 6e 0a 7c 07 7c ...\...}.}.}.|.|.d.k(..r.d.n.|.|
3be0 09 7c 09 64 02 7a 0a 00 00 7a 05 00 00 7a 0b 00 00 93 02 8c 1b 04 00 7d 08 7d 09 7d 04 7d 07 6e .|.d.z...z...z.........}.}.}.}.n
3c00 37 74 09 00 00 00 00 00 00 00 00 7c 00 7c 01 ab 02 00 00 00 00 00 00 7d 03 7c 03 44 00 8f 04 8f 7t.........|.|.........}.|.D....
3c20 09 8f 07 8f 0a 63 05 69 00 63 02 5d 1a 00 00 5c 04 00 00 7d 04 7d 09 7d 07 7d 0a 7c 04 7c 07 64 .....c.i.c.]...\...}.}.}.}.|.|.d
3c40 01 6b 28 00 00 72 02 64 01 6e 0a 7c 07 7c 09 7c 09 64 02 7a 0a 00 00 7a 05 00 00 7a 0b 00 00 93 .k(..r.d.n.|.|.|.d.z...z...z....
3c60 02 8c 1c 04 00 7d 08 7d 07 7d 09 7d 04 7d 0a 7c 01 7c 00 76 00 72 05 7c 08 7c 01 19 00 00 00 53 .....}.}.}.}.}.|.|.v.r.|.|.....S
3c80 00 7c 08 53 00 63 02 01 00 63 05 7d 07 7d 06 7d 05 7d 04 77 00 63 02 01 00 63 05 7d 07 7d 06 7d .|.S.c...c.}.}.}.}.w.c...c.}.}.}
3ca0 05 7d 04 77 00 63 02 01 00 63 04 7d 07 7d 09 7d 04 77 00 63 02 01 00 63 05 7d 0a 7d 07 7d 09 7d .}.w.c...c.}.}.}.w.c...c.}.}.}.}
3cc0 04 77 00 29 04 75 5d 0c 00 00 43 6f 6d 70 75 74 65 20 74 68 65 20 63 6c 75 73 74 65 72 69 6e 67 .w.).u]...Compute.the.clustering
3ce0 20 63 6f 65 66 66 69 63 69 65 6e 74 20 66 6f 72 20 6e 6f 64 65 73 2e 0a 0a 20 20 20 20 46 6f 72 .coefficient.for.nodes.......For
3d00 20 75 6e 77 65 69 67 68 74 65 64 20 67 72 61 70 68 73 2c 20 74 68 65 20 63 6c 75 73 74 65 72 69 .unweighted.graphs,.the.clusteri
3d20 6e 67 20 6f 66 20 61 20 6e 6f 64 65 20 3a 6d 61 74 68 3a 60 75 60 0a 20 20 20 20 69 73 20 74 68 ng.of.a.node.:math:`u`.....is.th
3d40 65 20 66 72 61 63 74 69 6f 6e 20 6f 66 20 70 6f 73 73 69 62 6c 65 20 74 72 69 61 6e 67 6c 65 73 e.fraction.of.possible.triangles
3d60 20 74 68 72 6f 75 67 68 20 74 68 61 74 20 6e 6f 64 65 20 74 68 61 74 20 65 78 69 73 74 2c 0a 0a .through.that.node.that.exist,..
3d80 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 0a 0a 20 20 20 20 20 20 63 5f 75 20 3d 20 5c 66 72 61 63 .......math::........c_u.=.\frac
3da0 7b 32 20 54 28 75 29 7d 7b 64 65 67 28 75 29 28 64 65 67 28 75 29 2d 31 29 7d 2c 0a 0a 20 20 20 {2.T(u)}{deg(u)(deg(u)-1)},.....
3dc0 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 54 28 75 29 60 20 69 73 20 74 68 65 20 6e 75 6d 62 65 .where.:math:`T(u)`.is.the.numbe
3de0 72 20 6f 66 20 74 72 69 61 6e 67 6c 65 73 20 74 68 72 6f 75 67 68 20 6e 6f 64 65 20 3a 6d 61 74 r.of.triangles.through.node.:mat
3e00 68 3a 60 75 60 20 61 6e 64 0a 20 20 20 20 3a 6d 61 74 68 3a 60 64 65 67 28 75 29 60 20 69 73 20 h:`u`.and.....:math:`deg(u)`.is.
3e20 74 68 65 20 64 65 67 72 65 65 20 6f 66 20 3a 6d 61 74 68 3a 60 75 60 2e 0a 0a 20 20 20 20 46 6f the.degree.of.:math:`u`.......Fo
3e40 72 20 77 65 69 67 68 74 65 64 20 67 72 61 70 68 73 2c 20 74 68 65 72 65 20 61 72 65 20 73 65 76 r.weighted.graphs,.there.are.sev
3e60 65 72 61 6c 20 77 61 79 73 20 74 6f 20 64 65 66 69 6e 65 20 63 6c 75 73 74 65 72 69 6e 67 20 5b eral.ways.to.define.clustering.[
3e80 31 5d 5f 2e 0a 20 20 20 20 74 68 65 20 6f 6e 65 20 75 73 65 64 20 68 65 72 65 20 69 73 20 64 65 1]_......the.one.used.here.is.de
3ea0 66 69 6e 65 64 0a 20 20 20 20 61 73 20 74 68 65 20 67 65 6f 6d 65 74 72 69 63 20 61 76 65 72 61 fined.....as.the.geometric.avera
3ec0 67 65 20 6f 66 20 74 68 65 20 73 75 62 67 72 61 70 68 20 65 64 67 65 20 77 65 69 67 68 74 73 20 ge.of.the.subgraph.edge.weights.
3ee0 5b 32 5d 5f 2c 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 0a 0a 20 20 20 20 20 20 20 63 5f 75 [2]_,.........math::.........c_u
3f00 20 3d 20 5c 66 72 61 63 7b 31 7d 7b 64 65 67 28 75 29 28 64 65 67 28 75 29 2d 31 29 29 7d 0a 20 .=.\frac{1}{deg(u)(deg(u)-1))}..
3f20 20 20 20 20 20 20 20 20 20 20 20 20 5c 73 75 6d 5f 7b 76 77 7d 20 28 5c 68 61 74 7b 77 7d 5f 7b ............\sum_{vw}.(\hat{w}_{
3f40 75 76 7d 20 5c 68 61 74 7b 77 7d 5f 7b 75 77 7d 20 5c 68 61 74 7b 77 7d 5f 7b 76 77 7d 29 5e 7b uv}.\hat{w}_{uw}.\hat{w}_{vw})^{
3f60 31 2f 33 7d 2e 0a 0a 20 20 20 20 54 68 65 20 65 64 67 65 20 77 65 69 67 68 74 73 20 3a 6d 61 74 1/3}.......The.edge.weights.:mat
3f80 68 3a 60 5c 68 61 74 7b 77 7d 5f 7b 75 76 7d 60 20 61 72 65 20 6e 6f 72 6d 61 6c 69 7a 65 64 20 h:`\hat{w}_{uv}`.are.normalized.
3fa0 62 79 20 74 68 65 20 6d 61 78 69 6d 75 6d 20 77 65 69 67 68 74 0a 20 20 20 20 69 6e 20 74 68 65 by.the.maximum.weight.....in.the
3fc0 20 6e 65 74 77 6f 72 6b 20 3a 6d 61 74 68 3a 60 5c 68 61 74 7b 77 7d 5f 7b 75 76 7d 20 3d 20 77 .network.:math:`\hat{w}_{uv}.=.w
3fe0 5f 7b 75 76 7d 2f 5c 6d 61 78 28 77 29 60 2e 0a 0a 20 20 20 20 54 68 65 20 76 61 6c 75 65 20 6f _{uv}/\max(w)`.......The.value.o
4000 66 20 3a 6d 61 74 68 3a 60 63 5f 75 60 20 69 73 20 61 73 73 69 67 6e 65 64 20 74 6f 20 30 20 69 f.:math:`c_u`.is.assigned.to.0.i
4020 66 20 3a 6d 61 74 68 3a 60 64 65 67 28 75 29 20 3c 20 32 60 2e 0a 0a 20 20 20 20 41 64 64 69 74 f.:math:`deg(u).<.2`.......Addit
4040 69 6f 6e 61 6c 6c 79 2c 20 74 68 69 73 20 77 65 69 67 68 74 65 64 20 64 65 66 69 6e 69 74 69 6f ionally,.this.weighted.definitio
4060 6e 20 68 61 73 20 62 65 65 6e 20 67 65 6e 65 72 61 6c 69 7a 65 64 20 74 6f 20 73 75 70 70 6f 72 n.has.been.generalized.to.suppor
4080 74 20 6e 65 67 61 74 69 76 65 20 65 64 67 65 20 77 65 69 67 68 74 73 20 5b 33 5d 5f 2e 0a 0a 20 t.negative.edge.weights.[3]_....
40a0 20 20 20 46 6f 72 20 64 69 72 65 63 74 65 64 20 67 72 61 70 68 73 2c 20 74 68 65 20 63 6c 75 73 ...For.directed.graphs,.the.clus
40c0 74 65 72 69 6e 67 20 69 73 20 73 69 6d 69 6c 61 72 6c 79 20 64 65 66 69 6e 65 64 20 61 73 20 74 tering.is.similarly.defined.as.t
40e0 68 65 20 66 72 61 63 74 69 6f 6e 0a 20 20 20 20 6f 66 20 61 6c 6c 20 70 6f 73 73 69 62 6c 65 20 he.fraction.....of.all.possible.
4100 64 69 72 65 63 74 65 64 20 74 72 69 61 6e 67 6c 65 73 20 6f 72 20 67 65 6f 6d 65 74 72 69 63 20 directed.triangles.or.geometric.
4120 61 76 65 72 61 67 65 20 6f 66 20 74 68 65 20 73 75 62 67 72 61 70 68 0a 20 20 20 20 65 64 67 65 average.of.the.subgraph.....edge
4140 20 77 65 69 67 68 74 73 20 66 6f 72 20 75 6e 77 65 69 67 68 74 65 64 20 61 6e 64 20 77 65 69 67 .weights.for.unweighted.and.weig
4160 68 74 65 64 20 64 69 72 65 63 74 65 64 20 67 72 61 70 68 20 72 65 73 70 65 63 74 69 76 65 6c 79 hted.directed.graph.respectively
4180 20 5b 34 5d 5f 2e 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 0a 0a 20 20 20 20 20 20 20 63 5f .[4]_..........math::.........c_
41a0 75 20 3d 20 5c 66 72 61 63 7b 54 28 75 29 7d 7b 32 28 64 65 67 5e 7b 74 6f 74 7d 28 75 29 28 64 u.=.\frac{T(u)}{2(deg^{tot}(u)(d
41c0 65 67 5e 7b 74 6f 74 7d 28 75 29 2d 31 29 20 2d 20 32 64 65 67 5e 7b 5c 6c 65 66 74 72 69 67 68 eg^{tot}(u)-1).-.2deg^{\leftrigh
41e0 74 61 72 72 6f 77 7d 28 75 29 29 7d 2c 0a 0a 20 20 20 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 tarrow}(u))},......where.:math:`
4200 54 28 75 29 60 20 69 73 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 64 69 72 65 63 74 65 64 20 T(u)`.is.the.number.of.directed.
4220 74 72 69 61 6e 67 6c 65 73 20 74 68 72 6f 75 67 68 20 6e 6f 64 65 0a 20 20 20 20 3a 6d 61 74 68 triangles.through.node.....:math
4240 3a 60 75 60 2c 20 3a 6d 61 74 68 3a 60 64 65 67 5e 7b 74 6f 74 7d 28 75 29 60 20 69 73 20 74 68 :`u`,.:math:`deg^{tot}(u)`.is.th
4260 65 20 73 75 6d 20 6f 66 20 69 6e 20 64 65 67 72 65 65 20 61 6e 64 20 6f 75 74 20 64 65 67 72 65 e.sum.of.in.degree.and.out.degre
4280 65 20 6f 66 0a 20 20 20 20 3a 6d 61 74 68 3a 60 75 60 20 61 6e 64 20 3a 6d 61 74 68 3a 60 64 65 e.of.....:math:`u`.and.:math:`de
42a0 67 5e 7b 5c 6c 65 66 74 72 69 67 68 74 61 72 72 6f 77 7d 28 75 29 60 20 69 73 20 74 68 65 20 72 g^{\leftrightarrow}(u)`.is.the.r
42c0 65 63 69 70 72 6f 63 61 6c 20 64 65 67 72 65 65 20 6f 66 0a 20 20 20 20 3a 6d 61 74 68 3a 60 75 eciprocal.degree.of.....:math:`u
42e0 60 2e 0a 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 2d 2d `........Parameters.....--------
4300 2d 2d 0a 20 20 20 20 47 20 3a 20 67 72 61 70 68 0a 0a 20 20 20 20 6e 6f 64 65 73 20 3a 20 6e 6f --.....G.:.graph......nodes.:.no
4320 64 65 2c 20 69 74 65 72 61 62 6c 65 20 6f 66 20 6e 6f 64 65 73 2c 20 6f 72 20 4e 6f 6e 65 20 28 de,.iterable.of.nodes,.or.None.(
4340 64 65 66 61 75 6c 74 3d 4e 6f 6e 65 29 0a 20 20 20 20 20 20 20 20 49 66 20 61 20 73 69 6e 67 6c default=None).........If.a.singl
4360 65 74 6f 6e 20 6e 6f 64 65 2c 20 72 65 74 75 72 6e 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 eton.node,.return.the.number.of.
4380 74 72 69 61 6e 67 6c 65 73 20 66 6f 72 20 74 68 61 74 20 6e 6f 64 65 2e 0a 20 20 20 20 20 20 20 triangles.for.that.node.........
43a0 20 49 66 20 61 6e 20 69 74 65 72 61 62 6c 65 2c 20 63 6f 6d 70 75 74 65 20 74 68 65 20 6e 75 6d .If.an.iterable,.compute.the.num
43c0 62 65 72 20 6f 66 20 74 72 69 61 6e 67 6c 65 73 20 66 6f 72 20 65 61 63 68 20 6f 66 20 74 68 6f ber.of.triangles.for.each.of.tho
43e0 73 65 20 6e 6f 64 65 73 2e 0a 20 20 20 20 20 20 20 20 49 66 20 60 4e 6f 6e 65 60 20 28 74 68 65 se.nodes..........If.`None`.(the
4400 20 64 65 66 61 75 6c 74 29 20 63 6f 6d 70 75 74 65 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 .default).compute.the.number.of.
4420 74 72 69 61 6e 67 6c 65 73 20 66 6f 72 20 61 6c 6c 20 6e 6f 64 65 73 20 69 6e 20 60 47 60 2e 0a triangles.for.all.nodes.in.`G`..
4440 0a 20 20 20 20 77 65 69 67 68 74 20 3a 20 73 74 72 69 6e 67 20 6f 72 20 4e 6f 6e 65 2c 20 6f 70 .....weight.:.string.or.None,.op
4460 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 20 20 20 20 54 68 65 tional.(default=None)........The
4480 20 65 64 67 65 20 61 74 74 72 69 62 75 74 65 20 74 68 61 74 20 68 6f 6c 64 73 20 74 68 65 20 6e .edge.attribute.that.holds.the.n
44a0 75 6d 65 72 69 63 61 6c 20 76 61 6c 75 65 20 75 73 65 64 20 61 73 20 61 20 77 65 69 67 68 74 2e umerical.value.used.as.a.weight.
44c0 0a 20 20 20 20 20 20 20 49 66 20 4e 6f 6e 65 2c 20 74 68 65 6e 20 65 61 63 68 20 65 64 67 65 20 ........If.None,.then.each.edge.
44e0 68 61 73 20 77 65 69 67 68 74 20 31 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d has.weight.1.......Returns.....-
4500 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6f 75 74 20 3a 20 66 6c 6f 61 74 2c 20 6f 72 20 64 69 63 74 69 ------.....out.:.float,.or.dicti
4520 6f 6e 61 72 79 0a 20 20 20 20 20 20 20 43 6c 75 73 74 65 72 69 6e 67 20 63 6f 65 66 66 69 63 69 onary........Clustering.coeffici
4540 65 6e 74 20 61 74 20 73 70 65 63 69 66 69 65 64 20 6e 6f 64 65 73 0a 0a 20 20 20 20 45 78 61 6d ent.at.specified.nodes......Exam
4560 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 47 20 3d 20 6e 78 ples.....--------.....>>>.G.=.nx
4580 2e 63 6f 6d 70 6c 65 74 65 5f 67 72 61 70 68 28 35 29 0a 20 20 20 20 3e 3e 3e 20 70 72 69 6e 74 .complete_graph(5).....>>>.print
45a0 28 6e 78 2e 63 6c 75 73 74 65 72 69 6e 67 28 47 2c 20 30 29 29 0a 20 20 20 20 31 2e 30 0a 20 20 (nx.clustering(G,.0)).....1.0...
45c0 20 20 3e 3e 3e 20 70 72 69 6e 74 28 6e 78 2e 63 6c 75 73 74 65 72 69 6e 67 28 47 29 29 0a 20 20 ..>>>.print(nx.clustering(G))...
45e0 20 20 7b 30 3a 20 31 2e 30 2c 20 31 3a 20 31 2e 30 2c 20 32 3a 20 31 2e 30 2c 20 33 3a 20 31 2e ..{0:.1.0,.1:.1.0,.2:.1.0,.3:.1.
4600 30 2c 20 34 3a 20 31 2e 30 7d 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 0,.4:.1.0}......Notes.....-----.
4620 20 20 20 20 53 65 6c 66 20 6c 6f 6f 70 73 20 61 72 65 20 69 67 6e 6f 72 65 64 2e 0a 0a 20 20 20 ....Self.loops.are.ignored......
4640 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 20 20 20 20 2e .References.....----------......
4660 2e 20 5b 31 5d 20 47 65 6e 65 72 61 6c 69 7a 61 74 69 6f 6e 73 20 6f 66 20 74 68 65 20 63 6c 75 ..[1].Generalizations.of.the.clu
4680 73 74 65 72 69 6e 67 20 63 6f 65 66 66 69 63 69 65 6e 74 20 74 6f 20 77 65 69 67 68 74 65 64 0a stering.coefficient.to.weighted.
46a0 20 20 20 20 20 20 20 63 6f 6d 70 6c 65 78 20 6e 65 74 77 6f 72 6b 73 20 62 79 20 4a 2e 20 53 61 .......complex.networks.by.J..Sa
46c0 72 61 6d c3 a4 6b 69 2c 20 4d 2e 20 4b 69 76 65 6c c3 a4 2c 20 4a 2e 2d 50 2e 20 4f 6e 6e 65 6c ram..ki,.M..Kivel..,.J.-P..Onnel
46e0 61 2c 0a 20 20 20 20 20 20 20 4b 2e 20 4b 61 73 6b 69 2c 20 61 6e 64 20 4a 2e 20 4b 65 72 74 c3 a,........K..Kaski,.and.J..Kert.
4700 a9 73 7a 2c 20 50 68 79 73 69 63 61 6c 20 52 65 76 69 65 77 20 45 2c 20 37 35 20 30 32 37 31 30 .sz,.Physical.Review.E,.75.02710
4720 35 20 28 32 30 30 37 29 2e 0a 20 20 20 20 20 20 20 68 74 74 70 3a 2f 2f 6a 70 6f 6e 6e 65 6c 61 5.(2007).........http://jponnela
4740 2e 63 6f 6d 2f 77 65 62 5f 64 6f 63 75 6d 65 6e 74 73 2f 61 39 2e 70 64 66 0a 20 20 20 20 2e 2e .com/web_documents/a9.pdf.......
4760 20 5b 32 5d 20 49 6e 74 65 6e 73 69 74 79 20 61 6e 64 20 63 6f 68 65 72 65 6e 63 65 20 6f 66 20 .[2].Intensity.and.coherence.of.
4780 6d 6f 74 69 66 73 20 69 6e 20 77 65 69 67 68 74 65 64 20 63 6f 6d 70 6c 65 78 0a 20 20 20 20 20 motifs.in.weighted.complex......
47a0 20 20 6e 65 74 77 6f 72 6b 73 20 62 79 20 4a 2e 20 50 2e 20 4f 6e 6e 65 6c 61 2c 20 4a 2e 20 53 ..networks.by.J..P..Onnela,.J..S
47c0 61 72 61 6d c3 a4 6b 69 2c 20 4a 2e 20 4b 65 72 74 c3 a9 73 7a 2c 20 61 6e 64 20 4b 2e 20 4b 61 aram..ki,.J..Kert..sz,.and.K..Ka
47e0 73 6b 69 2c 0a 20 20 20 20 20 20 20 50 68 79 73 69 63 61 6c 20 52 65 76 69 65 77 20 45 2c 20 37 ski,........Physical.Review.E,.7
4800 31 28 36 29 2c 20 30 36 35 31 30 33 20 28 32 30 30 35 29 2e 0a 20 20 20 20 2e 2e 20 5b 33 5d 20 1(6),.065103.(2005).........[3].
4820 47 65 6e 65 72 61 6c 69 7a 61 74 69 6f 6e 20 6f 66 20 43 6c 75 73 74 65 72 69 6e 67 20 43 6f 65 Generalization.of.Clustering.Coe
4840 66 66 69 63 69 65 6e 74 73 20 74 6f 20 53 69 67 6e 65 64 20 43 6f 72 72 65 6c 61 74 69 6f 6e 20 fficients.to.Signed.Correlation.
4860 4e 65 74 77 6f 72 6b 73 0a 20 20 20 20 20 20 20 62 79 20 47 2e 20 43 6f 73 74 61 6e 74 69 6e 69 Networks........by.G..Costantini
4880 20 61 6e 64 20 4d 2e 20 50 65 72 75 67 69 6e 69 2c 20 50 6c 6f 53 20 6f 6e 65 2c 20 39 28 32 29 .and.M..Perugini,.PloS.one,.9(2)
48a0 2c 20 65 38 38 36 36 39 20 28 32 30 31 34 29 2e 0a 20 20 20 20 2e 2e 20 5b 34 5d 20 43 6c 75 73 ,.e88669.(2014).........[4].Clus
48c0 74 65 72 69 6e 67 20 69 6e 20 63 6f 6d 70 6c 65 78 20 64 69 72 65 63 74 65 64 20 6e 65 74 77 6f tering.in.complex.directed.netwo
48e0 72 6b 73 20 62 79 20 47 2e 20 46 61 67 69 6f 6c 6f 2c 0a 20 20 20 20 20 20 20 50 68 79 73 69 63 rks.by.G..Fagiolo,........Physic
4900 61 6c 20 52 65 76 69 65 77 20 45 2c 20 37 36 28 32 29 2c 20 30 32 36 31 30 37 20 28 32 30 30 37 al.Review.E,.76(2),.026107.(2007
4920 29 2e 0a 20 20 20 20 72 02 00 00 00 72 42 00 00 00 72 0f 00 00 00 29 05 da 0b 69 73 5f 64 69 72 )......r....rB...r....)...is_dir
4940 65 63 74 65 64 72 7c 00 00 00 72 77 00 00 00 72 65 00 00 00 72 11 00 00 00 29 0b 72 18 00 00 00 ectedr|...rw...re...r....).r....
4960 72 19 00 00 00 72 40 00 00 00 da 07 74 64 5f 69 74 65 72 72 1a 00 00 00 da 02 64 74 da 02 64 62 r....r@.....td_iterr......dt..db
4980 72 1c 00 00 00 da 08 63 6c 75 73 74 65 72 63 72 1b 00 00 00 72 1d 00 00 00 73 0b 00 00 00 20 20 r......clustercr....r....s......
49a0 20 20 20 20 20 20 20 20 20 72 27 00 00 00 72 09 00 00 00 72 09 00 00 00 36 01 00 00 73 94 01 00 .........r'...r....r....6...s...
49c0 00 80 00 f0 70 02 00 08 09 87 7d 81 7d 84 7f d8 0b 11 d0 0b 1d dc 16 42 c0 31 c0 65 c8 56 d3 16 ....p.....}.}..........B.1.e.V..
49e0 54 88 47 f0 06 00 25 2c f7 05 03 18 0e f1 00 03 18 0e e1 14 20 90 41 90 72 98 32 98 71 f0 03 00 T.G...%,..............A.r.2.q...
4a00 11 12 98 01 98 51 9a 06 91 31 a0 41 a8 22 b0 02 b0 51 b1 06 a9 2d b8 21 b8 62 b9 26 d1 2a 40 c0 .....Q...1.A."...Q...-.!.b.&.*@.
4a20 41 d1 29 45 d1 24 46 d1 10 46 f0 03 03 18 0e 88 48 f4 00 03 18 0e f4 0a 00 17 3a b8 21 b8 55 d3 A.)E.$F..F......H.........:.!.U.
4a40 16 43 88 47 f0 06 00 25 2c f7 05 03 18 0e f1 00 03 18 0e e1 14 20 90 41 90 72 98 32 98 71 f0 03 .C.G...%,..............A.r.2.q..
4a60 00 11 12 98 01 98 51 9a 06 91 31 a0 41 a8 22 b0 02 b0 51 b1 06 a9 2d b8 21 b8 62 b9 26 d1 2a 40 ......Q...1.A."...Q...-.!.b.&.*@
4a80 c0 41 d1 29 45 d1 24 46 d1 10 46 f0 03 03 18 0e 88 48 f4 00 03 18 0e f0 0c 00 0c 12 d0 0b 1d dc .A.)E.$F..F......H..............
4aa0 16 39 b8 21 b8 55 c0 46 d3 16 4b 88 47 d8 4d 54 d7 17 55 d0 17 55 c1 27 c0 21 c0 51 c8 01 98 01 .9.!.U.F..K.G.MT..U..U.'.!.Q....
4ac0 a0 01 a0 51 a2 06 99 31 a8 41 b0 11 b0 61 b8 21 b1 65 b1 1b d1 2c 3d d1 18 3d d0 17 55 88 48 d3 ...Q...1.A...a.!.e...,=..=..U.H.
4ae0 17 55 e4 16 30 b0 11 b0 45 d3 16 3a 88 47 d8 50 57 d7 17 58 d1 17 58 c1 2a c0 21 c0 51 c8 01 c8 .U..0...E..:.G.PW..X..X.*.!.Q...
4b00 31 98 01 a0 01 a0 51 a2 06 99 31 a8 41 b0 11 b0 61 b8 21 b1 65 b1 1b d1 2c 3d d1 18 3d d0 17 58 1.....Q...1.A...a.!.e...,=..=..X
4b20 88 48 d3 17 58 d8 07 0c 90 01 81 7a e0 0f 17 98 05 89 7f d0 08 1e d8 0b 13 80 4f f9 f5 2b 03 18 .H..X......z..............O..+..
4b40 0e f9 f5 0c 03 18 0e f9 f4 10 00 18 56 01 f9 f5 06 00 18 59 01 73 17 00 00 00 a7 28 44 10 0a c1 ............V......Y.s.....(D...
4b60 28 28 44 18 0a c2 2b 1e 44 20 08 c3 21 1f 44 27 0a 63 01 00 00 00 00 00 00 00 00 00 00 00 0a 00 ((D...+.D...!.D'.c..............
4b80 00 00 03 00 00 00 f3 d0 00 00 00 97 00 74 01 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 .............t.........|........
4ba0 00 44 00 8f 01 8f 02 8f 03 8f 04 63 05 67 00 63 02 5d 11 00 00 5c 04 00 00 7d 01 7d 02 7d 03 7d .D.........c.g.c.]...\...}.}.}.}
4bc0 04 7c 03 7c 02 7c 02 64 01 7a 0a 00 00 7a 05 00 00 66 02 91 02 8c 13 04 00 7d 05 7d 03 7d 02 7d .|.|.|.d.z...z...f.......}.}.}.}
4be0 01 7d 04 74 03 00 00 00 00 00 00 00 00 7c 05 ab 01 00 00 00 00 00 00 64 02 6b 28 00 00 72 01 79 .}.t.........|.........d.k(..r.y
4c00 02 74 05 00 00 00 00 00 00 00 00 74 06 00 00 00 00 00 00 00 00 74 09 00 00 00 00 00 00 00 00 7c .t.........t.........t.........|
4c20 05 8e 00 ab 02 00 00 00 00 00 00 5c 02 00 00 7d 06 7d 07 7c 06 64 02 6b 28 00 00 72 02 64 02 53 ...........\...}.}.|.d.k(..r.d.S
4c40 00 7c 06 7c 07 7a 0b 00 00 53 00 63 02 01 00 63 05 7d 04 7d 03 7d 02 7d 01 77 00 29 03 61 15 02 .|.|.z...S.c...c.}.}.}.}.w.).a..
4c60 00 00 43 6f 6d 70 75 74 65 20 67 72 61 70 68 20 74 72 61 6e 73 69 74 69 76 69 74 79 2c 20 74 68 ..Compute.graph.transitivity,.th
4c80 65 20 66 72 61 63 74 69 6f 6e 20 6f 66 20 61 6c 6c 20 70 6f 73 73 69 62 6c 65 20 74 72 69 61 6e e.fraction.of.all.possible.trian
4ca0 67 6c 65 73 0a 20 20 20 20 70 72 65 73 65 6e 74 20 69 6e 20 47 2e 0a 0a 20 20 20 20 50 6f 73 73 gles.....present.in.G.......Poss
4cc0 69 62 6c 65 20 74 72 69 61 6e 67 6c 65 73 20 61 72 65 20 69 64 65 6e 74 69 66 69 65 64 20 62 79 ible.triangles.are.identified.by
4ce0 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 22 74 72 69 61 64 73 22 0a 20 20 20 20 28 74 77 6f .the.number.of."triads".....(two
4d00 20 65 64 67 65 73 20 77 69 74 68 20 61 20 73 68 61 72 65 64 20 76 65 72 74 65 78 29 2e 0a 0a 20 .edges.with.a.shared.vertex)....
4d20 20 20 20 54 68 65 20 74 72 61 6e 73 69 74 69 76 69 74 79 20 69 73 0a 0a 20 20 20 20 2e 2e 20 6d ...The.transitivity.is.........m
4d40 61 74 68 3a 3a 0a 0a 20 20 20 20 20 20 20 20 54 20 3d 20 33 5c 66 72 61 63 7b 5c 23 74 72 69 61 ath::..........T.=.3\frac{\#tria
4d60 6e 67 6c 65 73 7d 7b 5c 23 74 72 69 61 64 73 7d 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 ngles}{\#triads}.......Parameter
4d80 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 0a 0a s.....----------.....G.:.graph..
4da0 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 6f 75 74 20 ....Returns.....-------.....out.
4dc0 3a 20 66 6c 6f 61 74 0a 20 20 20 20 20 20 20 54 72 61 6e 73 69 74 69 76 69 74 79 0a 0a 20 20 20 :.float........Transitivity.....
4de0 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 53 65 6c 66 20 6c 6f 6f 70 73 20 .Notes.....-----.....Self.loops.
4e00 61 72 65 20 69 67 6e 6f 72 65 64 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d are.ignored.......Examples.....-
4e20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 63 6f 6d 70 6c 65 74 65 5f -------.....>>>.G.=.nx.complete_
4e40 67 72 61 70 68 28 35 29 0a 20 20 20 20 3e 3e 3e 20 70 72 69 6e 74 28 6e 78 2e 74 72 61 6e 73 69 graph(5).....>>>.print(nx.transi
4e60 74 69 76 69 74 79 28 47 29 29 0a 20 20 20 20 31 2e 30 0a 20 20 20 20 72 42 00 00 00 72 02 00 00 tivity(G)).....1.0.....rB...r...
4e80 00 29 05 72 11 00 00 00 72 16 00 00 00 da 03 6d 61 70 72 3b 00 00 00 da 03 7a 69 70 29 08 72 18 .).r....r......mapr;.....zip).r.
4ea0 00 00 00 72 1a 00 00 00 72 1b 00 00 00 72 1c 00 00 00 72 1d 00 00 00 da 10 74 72 69 61 6e 67 6c ...r....r....r....r......triangl
4ec0 65 73 5f 63 6f 6e 74 72 69 72 07 00 00 00 da 06 63 6f 6e 74 72 69 73 08 00 00 00 20 20 20 20 20 es_contrir......contris.........
4ee0 20 20 20 72 27 00 00 00 72 0a 00 00 00 72 0a 00 00 00 a9 01 00 00 73 85 00 00 00 80 00 f4 44 01 ...r'...r....r........s.......D.
4f00 00 2c 46 01 c0 61 d3 2b 48 f7 03 02 18 06 f1 00 02 18 06 d9 1d 27 98 51 a0 01 a0 31 a0 61 88 11 .,F..a.+H............'.Q...1.a..
4f20 88 41 90 11 90 51 91 15 89 4b d2 08 18 f0 03 02 18 06 d0 04 14 f3 00 02 18 06 f4 08 00 08 0b d0 .A...Q...K......................
4f40 0b 1b d3 07 1c a0 01 d2 07 21 d8 0f 10 dc 18 1b 9c 43 a4 13 d0 26 36 d0 21 37 d3 18 38 d1 04 15 .........!.......C...&6.!7..8...
4f60 80 49 88 76 d8 10 19 98 51 92 0e 88 31 d0 04 36 a0 49 b0 06 d1 24 36 d0 04 36 f9 f5 0f 02 18 06 .I.v....Q...1..6.I...$6..6......
4f80 73 05 00 00 00 91 16 41 20 0a 63 02 00 00 00 00 00 00 00 00 00 00 00 07 00 00 00 03 00 00 00 f3 s......A..c.....................
4fa0 6a 02 00 00 87 12 87 13 97 00 7c 01 80 03 7c 00 7d 02 6e 11 7c 00 6a 01 00 00 00 00 00 00 00 00 j.........|...|.}.n.|.j.........
4fc0 00 00 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 7d 02 69 00 7d 03 7c 00 6a 02 00 00 ..........|.........}.i.}.|.j...
4fe0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 8a 13 02 00 47 00 88 13 66 01 64 01 84 08 64 02 ....................G...f.d...d.
5000 74 04 00 00 00 00 00 00 00 00 ab 03 00 00 00 00 00 00 7d 04 02 00 7c 04 ab 00 00 00 00 00 00 00 t.................}...|.........
5020 8a 12 7c 02 44 00 5d e6 00 00 7d 05 89 12 7c 05 19 00 00 00 7d 06 74 07 00 00 00 00 00 00 00 00 ..|.D.]...}...|.....}.t.........
5040 7c 06 ab 01 00 00 00 00 00 00 64 03 7a 0a 00 00 7d 07 7c 07 64 04 6b 1a 00 00 72 06 64 04 7c 03 |.........d.z...}.|.d.k...r.d.|.
5060 7c 05 3c 00 00 00 8c 21 64 04 7d 08 74 07 00 00 00 00 00 00 00 00 7c 06 ab 01 00 00 00 00 00 00 |.<....!d.}.t.........|.........
5080 7c 07 7a 05 00 00 7d 09 64 04 7d 0a 64 04 7d 0b 7c 06 44 00 5d 36 00 00 7d 0c 89 12 7c 0c 19 00 |.z...}.d.}.d.}.|.D.]6..}...|...
50a0 00 00 7d 0d 7c 08 74 07 00 00 00 00 00 00 00 00 7c 0d ab 01 00 00 00 00 00 00 7c 07 7a 05 00 00 ..}.|.t.........|.........|.z...
50c0 7a 0d 00 00 7d 08 74 07 00 00 00 00 00 00 00 00 7c 0d 7c 06 7a 01 00 00 ab 01 00 00 00 00 00 00 z...}.t.........|.|.z...........
50e0 7d 0e 7c 0a 7c 0e 7a 0d 00 00 7d 0a 7c 0b 7c 0e 7c 0e 64 03 7a 0a 00 00 7a 05 00 00 7a 0d 00 00 }.|.|.z...}.|.|.|.d.z...z...z...
5100 7d 0b 8c 38 04 00 74 09 00 00 00 00 00 00 00 00 6a 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 }..8..t.........j...............
5120 00 00 00 00 88 12 66 01 64 05 84 08 7c 06 44 00 ab 00 00 00 00 00 00 00 8e 00 7d 0f 7c 0f 7c 06 ......f.d...|.D...........}.|.|.
5140 7a 17 00 00 7d 0f 7c 0f 6a 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 05 ab 01 z...}.|.j...................|...
5160 00 00 00 00 00 00 01 00 7c 0f 44 00 5d 1e 00 00 7d 10 74 07 00 00 00 00 00 00 00 00 7c 06 89 12 ........|.D.]...}.t.........|...
5180 7c 10 19 00 00 00 7a 01 00 00 ab 01 00 00 00 00 00 00 7d 0e 7c 0b 7c 0e 7c 0e 64 03 7a 0a 00 00 |.....z...........}.|.|.|.d.z...
51a0 7a 05 00 00 7a 0d 00 00 7d 0b 8c 20 04 00 7c 0b 64 06 7a 0f 00 00 7d 0b 7c 08 7c 09 7a 0a 00 00 z...z...}.....|.d.z...}.|.|.z...
51c0 7c 0a 7a 0a 00 00 7c 0b 7a 0a 00 00 7d 11 7c 11 64 04 6b 44 00 00 72 09 7c 0b 7c 11 7a 0b 00 00 |.z...|.z...}.|.d.kD..r.|.|.z...
51e0 7c 03 7c 05 3c 00 00 00 8c e2 64 04 7c 03 7c 05 3c 00 00 00 8c e8 04 00 7c 01 7c 00 76 00 72 05 |.|.<.....d.|.|.<.......|.|.v.r.
5200 7c 03 7c 01 19 00 00 00 53 00 7c 03 53 00 29 07 75 82 07 00 00 43 6f 6d 70 75 74 65 20 74 68 65 |.|.....S.|.S.).u....Compute.the
5220 20 73 71 75 61 72 65 73 20 63 6c 75 73 74 65 72 69 6e 67 20 63 6f 65 66 66 69 63 69 65 6e 74 20 .squares.clustering.coefficient.
5240 66 6f 72 20 6e 6f 64 65 73 2e 0a 0a 20 20 20 20 46 6f 72 20 65 61 63 68 20 6e 6f 64 65 20 72 65 for.nodes.......For.each.node.re
5260 74 75 72 6e 20 74 68 65 20 66 72 61 63 74 69 6f 6e 20 6f 66 20 70 6f 73 73 69 62 6c 65 20 73 71 turn.the.fraction.of.possible.sq
5280 75 61 72 65 73 20 74 68 61 74 20 65 78 69 73 74 20 61 74 0a 20 20 20 20 74 68 65 20 6e 6f 64 65 uares.that.exist.at.....the.node
52a0 20 5b 31 5d 5f 0a 0a 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 0a 20 20 20 20 20 20 20 43 5f 34 28 .[1]_.........math::........C_4(
52c0 76 29 20 3d 20 5c 66 72 61 63 7b 20 5c 73 75 6d 5f 7b 75 3d 31 7d 5e 7b 6b 5f 76 7d 0a 20 20 20 v).=.\frac{.\sum_{u=1}^{k_v}....
52e0 20 20 20 20 5c 73 75 6d 5f 7b 77 3d 75 2b 31 7d 5e 7b 6b 5f 76 7d 20 71 5f 76 28 75 2c 77 29 20 ....\sum_{w=u+1}^{k_v}.q_v(u,w).
5300 7d 7b 20 5c 73 75 6d 5f 7b 75 3d 31 7d 5e 7b 6b 5f 76 7d 0a 20 20 20 20 20 20 20 5c 73 75 6d 5f }{.\sum_{u=1}^{k_v}........\sum_
5320 7b 77 3d 75 2b 31 7d 5e 7b 6b 5f 76 7d 20 5b 61 5f 76 28 75 2c 77 29 20 2b 20 71 5f 76 28 75 2c {w=u+1}^{k_v}.[a_v(u,w).+.q_v(u,
5340 77 29 5d 7d 2c 0a 0a 20 20 20 20 77 68 65 72 65 20 3a 6d 61 74 68 3a 60 71 5f 76 28 75 2c 77 29 w)]},......where.:math:`q_v(u,w)
5360 60 20 61 72 65 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 63 6f 6d 6d 6f 6e 20 6e 65 69 67 68 `.are.the.number.of.common.neigh
5380 62 6f 72 73 20 6f 66 20 3a 6d 61 74 68 3a 60 75 60 20 61 6e 64 0a 20 20 20 20 3a 6d 61 74 68 3a bors.of.:math:`u`.and.....:math:
53a0 60 77 60 20 6f 74 68 65 72 20 74 68 61 6e 20 3a 6d 61 74 68 3a 60 76 60 20 28 69 65 20 73 71 75 `w`.other.than.:math:`v`.(ie.squ
53c0 61 72 65 73 29 2c 20 61 6e 64 20 3a 6d 61 74 68 3a 60 61 5f 76 28 75 2c 77 29 20 3d 20 28 6b 5f ares),.and.:math:`a_v(u,w).=.(k_
53e0 75 20 2d 0a 20 20 20 20 28 31 2b 71 5f 76 28 75 2c 77 29 2b 5c 74 68 65 74 61 5f 7b 75 76 7d 29 u.-.....(1+q_v(u,w)+\theta_{uv})
5400 29 20 2b 20 28 6b 5f 77 20 2d 20 28 31 2b 71 5f 76 28 75 2c 77 29 2b 5c 74 68 65 74 61 5f 7b 75 ).+.(k_w.-.(1+q_v(u,w)+\theta_{u
5420 77 7d 29 29 60 2c 20 77 68 65 72 65 0a 20 20 20 20 3a 6d 61 74 68 3a 60 5c 74 68 65 74 61 5f 7b w}))`,.where.....:math:`\theta_{
5440 75 77 7d 20 3d 20 31 60 20 69 66 20 3a 6d 61 74 68 3a 60 75 60 20 61 6e 64 20 3a 6d 61 74 68 3a uw}.=.1`.if.:math:`u`.and.:math:
5460 60 77 60 20 61 72 65 20 63 6f 6e 6e 65 63 74 65 64 20 61 6e 64 20 30 0a 20 20 20 20 6f 74 68 65 `w`.are.connected.and.0.....othe
5480 72 77 69 73 65 2e 20 5b 32 5d 5f 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 rwise..[2]_......Parameters.....
54a0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 20 3a 20 67 72 61 70 68 0a 0a 20 20 20 20 6e 6f ----------.....G.:.graph......no
54c0 64 65 73 20 3a 20 63 6f 6e 74 61 69 6e 65 72 20 6f 66 20 6e 6f 64 65 73 2c 20 6f 70 74 69 6f 6e des.:.container.of.nodes,.option
54e0 61 6c 20 28 64 65 66 61 75 6c 74 3d 61 6c 6c 20 6e 6f 64 65 73 20 69 6e 20 47 29 0a 20 20 20 20 al.(default=all.nodes.in.G).....
5500 20 20 20 43 6f 6d 70 75 74 65 20 63 6c 75 73 74 65 72 69 6e 67 20 66 6f 72 20 6e 6f 64 65 73 20 ...Compute.clustering.for.nodes.
5520 69 6e 20 74 68 69 73 20 63 6f 6e 74 61 69 6e 65 72 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a in.this.container.......Returns.
5540 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 63 34 20 3a 20 64 69 63 74 69 6f 6e 61 72 79 0a ....-------.....c4.:.dictionary.
5560 20 20 20 20 20 20 20 41 20 64 69 63 74 69 6f 6e 61 72 79 20 6b 65 79 65 64 20 62 79 20 6e 6f 64 .......A.dictionary.keyed.by.nod
5580 65 20 77 69 74 68 20 74 68 65 20 73 71 75 61 72 65 20 63 6c 75 73 74 65 72 69 6e 67 20 63 6f 65 e.with.the.square.clustering.coe
55a0 66 66 69 63 69 65 6e 74 20 76 61 6c 75 65 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 fficient.value.......Examples...
55c0 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 63 6f 6d 70 6c 65 ..--------.....>>>.G.=.nx.comple
55e0 74 65 5f 67 72 61 70 68 28 35 29 0a 20 20 20 20 3e 3e 3e 20 70 72 69 6e 74 28 6e 78 2e 73 71 75 te_graph(5).....>>>.print(nx.squ
5600 61 72 65 5f 63 6c 75 73 74 65 72 69 6e 67 28 47 2c 20 30 29 29 0a 20 20 20 20 31 2e 30 0a 20 20 are_clustering(G,.0)).....1.0...
5620 20 20 3e 3e 3e 20 70 72 69 6e 74 28 6e 78 2e 73 71 75 61 72 65 5f 63 6c 75 73 74 65 72 69 6e 67 ..>>>.print(nx.square_clustering
5640 28 47 29 29 0a 20 20 20 20 7b 30 3a 20 31 2e 30 2c 20 31 3a 20 31 2e 30 2c 20 32 3a 20 31 2e 30 (G)).....{0:.1.0,.1:.1.0,.2:.1.0
5660 2c 20 33 3a 20 31 2e 30 2c 20 34 3a 20 31 2e 30 7d 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 ,.3:.1.0,.4:.1.0}......Notes....
5680 20 2d 2d 2d 2d 2d 0a 20 20 20 20 53 65 6c 66 20 6c 6f 6f 70 73 20 61 72 65 20 69 67 6e 6f 72 65 .-----.....Self.loops.are.ignore
56a0 64 2e 0a 0a 20 20 20 20 57 68 69 6c 65 20 3a 6d 61 74 68 3a 60 43 5f 33 28 76 29 60 20 28 74 72 d.......While.:math:`C_3(v)`.(tr
56c0 69 61 6e 67 6c 65 20 63 6c 75 73 74 65 72 69 6e 67 29 20 67 69 76 65 73 20 74 68 65 20 70 72 6f iangle.clustering).gives.the.pro
56e0 62 61 62 69 6c 69 74 79 20 74 68 61 74 0a 20 20 20 20 74 77 6f 20 6e 65 69 67 68 62 6f 72 73 20 bability.that.....two.neighbors.
5700 6f 66 20 6e 6f 64 65 20 76 20 61 72 65 20 63 6f 6e 6e 65 63 74 65 64 20 77 69 74 68 20 65 61 63 of.node.v.are.connected.with.eac
5720 68 20 6f 74 68 65 72 2c 20 3a 6d 61 74 68 3a 60 43 5f 34 28 76 29 60 20 69 73 0a 20 20 20 20 74 h.other,.:math:`C_4(v)`.is.....t
5740 68 65 20 70 72 6f 62 61 62 69 6c 69 74 79 20 74 68 61 74 20 74 77 6f 20 6e 65 69 67 68 62 6f 72 he.probability.that.two.neighbor
5760 73 20 6f 66 20 6e 6f 64 65 20 76 20 73 68 61 72 65 20 61 20 63 6f 6d 6d 6f 6e 0a 20 20 20 20 6e s.of.node.v.share.a.common.....n
5780 65 69 67 68 62 6f 72 20 64 69 66 66 65 72 65 6e 74 20 66 72 6f 6d 20 76 2e 20 54 68 69 73 20 61 eighbor.different.from.v..This.a
57a0 6c 67 6f 72 69 74 68 6d 20 63 61 6e 20 62 65 20 61 70 70 6c 69 65 64 20 74 6f 20 62 6f 74 68 0a lgorithm.can.be.applied.to.both.
57c0 20 20 20 20 62 69 70 61 72 74 69 74 65 20 61 6e 64 20 75 6e 69 70 61 72 74 69 74 65 20 6e 65 74 ....bipartite.and.unipartite.net
57e0 77 6f 72 6b 73 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 works.......References.....-----
5800 2d 2d 2d 2d 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 50 65 64 72 6f 20 47 2e 20 4c 69 6e 64 2c 20 -----........[1].Pedro.G..Lind,.
5820 4d 61 72 74 61 20 43 2e 20 47 6f 6e 7a c3 a1 6c 65 7a 2c 20 61 6e 64 20 48 61 6e 73 20 4a 2e 20 Marta.C..Gonz..lez,.and.Hans.J..
5840 48 65 72 72 6d 61 6e 6e 2e 20 32 30 30 35 0a 20 20 20 20 20 20 20 20 43 79 63 6c 65 73 20 61 6e Herrmann..2005.........Cycles.an
5860 64 20 63 6c 75 73 74 65 72 69 6e 67 20 69 6e 20 62 69 70 61 72 74 69 74 65 20 6e 65 74 77 6f 72 d.clustering.in.bipartite.networ
5880 6b 73 2e 0a 20 20 20 20 20 20 20 20 50 68 79 73 69 63 61 6c 20 52 65 76 69 65 77 20 45 20 28 37 ks..........Physical.Review.E.(7
58a0 32 29 20 30 35 36 31 32 37 2e 0a 20 20 20 20 2e 2e 20 5b 32 5d 20 5a 68 61 6e 67 2c 20 50 65 6e 2).056127.........[2].Zhang,.Pen
58c0 67 20 65 74 20 61 6c 2e 20 43 6c 75 73 74 65 72 69 6e 67 20 43 6f 65 66 66 69 63 69 65 6e 74 20 g.et.al..Clustering.Coefficient.
58e0 61 6e 64 20 43 6f 6d 6d 75 6e 69 74 79 20 53 74 72 75 63 74 75 72 65 20 6f 66 0a 20 20 20 20 20 and.Community.Structure.of......
5900 20 20 20 42 69 70 61 72 74 69 74 65 20 4e 65 74 77 6f 72 6b 73 2e 20 50 68 79 73 69 63 61 20 41 ...Bipartite.Networks..Physica.A
5920 3a 20 53 74 61 74 69 73 74 69 63 61 6c 20 4d 65 63 68 61 6e 69 63 73 20 61 6e 64 20 69 74 73 20 :.Statistical.Mechanics.and.its.
5940 41 70 70 6c 69 63 61 74 69 6f 6e 73 20 33 38 37 2e 32 37 20 28 32 30 30 38 29 3a 20 36 38 36 39 Applications.387.27.(2008):.6869
5960 e2 80 93 36 38 37 35 2e 0a 20 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 61 72 78 69 76 2e 6f ...6875..........https://arxiv.o
5980 72 67 2f 61 62 73 2f 30 37 31 30 2e 30 31 31 37 76 31 0a 20 20 20 20 63 00 00 00 00 00 00 00 00 rg/abs/0710.0117v1.....c........
59a0 00 00 00 00 02 00 00 00 00 00 00 00 f3 1c 00 00 00 95 01 97 00 65 00 5a 01 64 00 5a 02 64 01 5a .....................e.Z.d.Z.d.Z
59c0 03 88 00 66 01 64 02 84 08 5a 04 79 03 29 04 fa 1f 73 71 75 61 72 65 5f 63 6c 75 73 74 65 72 69 ...f.d...Z.y.)...square_clusteri
59e0 6e 67 2e 3c 6c 6f 63 61 6c 73 3e 2e 47 41 64 6a 7a 3e 43 61 6c 63 75 6c 61 74 65 20 28 61 6e 64 ng.<locals>.GAdjz>Calculate.(and
5a00 20 63 61 63 68 65 29 20 6e 6f 64 65 20 6e 65 69 67 68 62 6f 72 20 73 65 74 73 20 65 78 63 6c 75 .cache).node.neighbor.sets.exclu
5a20 64 69 6e 67 20 73 65 6c 66 2d 6c 6f 6f 70 73 2e 63 02 00 00 00 00 00 00 00 00 00 00 00 04 00 00 ding.self-loops.c...............
5a40 00 13 00 00 00 f3 50 00 00 00 95 01 97 00 74 01 00 00 00 00 00 00 00 00 89 03 7c 01 19 00 00 00 ......P.......t...........|.....
5a60 ab 01 00 00 00 00 00 00 78 01 7d 02 7c 00 7c 01 3c 00 00 00 7c 02 6a 03 00 00 00 00 00 00 00 00 ........x.}.|.|.<...|.j.........
5a80 00 00 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 01 00 7c 02 53 00 72 2b 00 00 00 29 ..........|...........|.S.r+...)
5aa0 02 72 33 00 00 00 da 07 64 69 73 63 61 72 64 29 04 da 04 73 65 6c 66 72 1a 00 00 00 da 0b 76 5f .r3.....discard)...selfr......v_
5ac0 6e 65 69 67 68 62 6f 72 73 da 06 5f 47 5f 61 64 6a 73 04 00 00 00 20 20 20 80 72 27 00 00 00 da neighbors.._G_adjs........r'....
5ae0 0b 5f 5f 6d 69 73 73 69 6e 67 5f 5f 7a 2b 73 71 75 61 72 65 5f 63 6c 75 73 74 65 72 69 6e 67 2e .__missing__z+square_clustering.
5b00 3c 6c 6f 63 61 6c 73 3e 2e 47 41 64 6a 2e 5f 5f 6d 69 73 73 69 6e 67 5f 5f 17 02 00 00 73 2d 00 <locals>.GAdj.__missing__....s-.
5b20 00 00 f8 80 00 dc 24 27 a8 06 a8 71 a9 09 a3 4e d0 0c 32 88 4b 98 24 98 71 99 27 d8 0c 17 d7 0c ......$'...q...N..2.K.$.q.'.....
5b40 1f d1 0c 1f a0 01 d4 0c 22 d8 13 1e d0 0c 1e 72 54 00 00 00 4e 29 05 da 08 5f 5f 6e 61 6d 65 5f ........"......rT...N)...__name_
5b60 5f da 0a 5f 5f 6d 6f 64 75 6c 65 5f 5f da 0c 5f 5f 71 75 61 6c 6e 61 6d 65 5f 5f da 07 5f 5f 64 _..__module__..__qualname__..__d
5b80 6f 63 5f 5f 72 96 00 00 00 29 01 72 95 00 00 00 73 01 00 00 00 80 72 27 00 00 00 da 04 47 41 64 oc__r....).r....s.....r'.....GAd
5ba0 6a 72 90 00 00 00 14 02 00 00 73 0b 00 00 00 f8 84 00 d9 08 4c f5 04 03 09 1f 72 54 00 00 00 72 jr........s.........L.....rT...r
5bc0 9b 00 00 00 72 42 00 00 00 72 02 00 00 00 63 01 00 00 00 00 00 00 00 00 00 00 00 03 00 00 00 33 ....rB...r....c................3
5be0 00 00 00 f3 28 00 00 00 95 01 4b 00 01 00 97 00 7c 00 5d 09 00 00 7d 01 89 02 7c 01 19 00 00 00 ....(.....K.....|.]...}...|.....
5c00 96 01 97 01 01 00 8c 0b 04 00 79 00 ad 03 77 01 72 2b 00 00 00 72 2c 00 00 00 29 03 72 2e 00 00 ..........y...w.r+...r,...).r...
5c20 00 72 48 00 00 00 da 05 47 5f 61 64 6a 73 03 00 00 00 20 20 80 72 27 00 00 00 72 2f 00 00 00 7a .rH.....G_adjs.......r'...r/...z
5c40 24 73 71 75 61 72 65 5f 63 6c 75 73 74 65 72 69 6e 67 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e $square_clustering.<locals>.<gen
5c60 65 78 70 72 3e 40 02 00 00 73 15 00 00 00 f8 e8 00 f8 80 00 d2 27 46 b0 51 a8 05 a8 61 ad 08 d1 expr>@...s...........'F.Q...a...
5c80 27 46 f9 73 04 00 00 00 83 0f 12 01 72 0f 00 00 00 29 07 72 3a 00 00 00 da 04 5f 61 64 6a 72 13 'F.s........r....).r:....._adjr.
5ca0 00 00 00 72 16 00 00 00 72 33 00 00 00 da 05 75 6e 69 6f 6e 72 92 00 00 00 29 14 72 18 00 00 00 ...r....r3.....unionr....).r....
5cc0 72 19 00 00 00 da 09 6e 6f 64 65 5f 69 74 65 72 72 09 00 00 00 72 9b 00 00 00 72 1a 00 00 00 72 r......node_iterr....r....r....r
5ce0 94 00 00 00 da 0c 76 5f 64 65 67 72 65 65 73 5f 6d 31 da 0a 75 77 5f 64 65 67 72 65 65 73 da 08 ......v_degrees_m1..uw_degrees..
5d00 75 77 5f 63 6f 75 6e 74 72 07 00 00 00 da 07 73 71 75 61 72 65 73 72 48 00 00 00 da 0b 75 5f 6e uw_countr......squaresrH.....u_n
5d20 65 69 67 68 62 6f 72 73 da 02 70 32 da 11 74 77 6f 5f 68 6f 70 5f 6e 65 69 67 68 62 6f 72 73 da eighbors..p2..two_hop_neighbors.
5d40 01 78 da 09 70 6f 74 65 6e 74 69 61 6c 72 9d 00 00 00 72 95 00 00 00 73 14 00 00 00 20 20 20 20 .x..potentialr....r....s........
5d60 20 20 20 20 20 20 20 20 20 20 20 20 20 20 40 40 72 27 00 00 00 72 0b 00 00 00 72 0b 00 00 00 d4 ..............@@r'...r....r.....
5d80 01 00 00 73 b5 01 00 00 f9 80 00 f0 72 01 00 08 0d 80 7d d8 14 15 89 09 e0 14 15 97 4d 91 4d a0 ...s........r.....}.........M.M.
5da0 25 d3 14 28 88 09 d8 11 13 80 4a d8 0d 0e 8f 56 89 56 80 46 f6 04 06 05 1f 8c 74 f4 00 06 05 1f %..(......J....V.V.F......t.....
5dc0 f1 10 00 0d 11 8b 46 80 45 e0 0d 16 f2 00 2e 05 1e 88 01 d8 16 1b 98 41 91 68 88 0b dc 17 1a 98 ......F.E..............A.h......
5de0 3b d3 17 27 a8 21 d1 17 2b 88 0c d8 0b 17 98 31 d2 0b 1c e0 1c 1d 88 4a 90 71 89 4d d8 0c 14 f0 ;..'.!..+......1.......J.q.M....
5e00 0a 00 16 17 88 0a e4 13 16 90 7b d3 13 23 a0 6c d1 13 32 88 08 e0 14 15 88 09 e0 12 13 88 07 f0 ..........{..#.l..2.............
5e20 06 00 12 1d f2 00 0a 09 25 88 41 d8 1a 1f a0 01 99 28 88 4b d8 0c 16 9c 23 98 6b d3 1a 2a a8 5c ........%.A......(.K....#.k..*.\
5e40 d1 1a 39 d1 0c 39 88 4a e4 11 14 90 5b a0 3b d1 15 2e d3 11 2f 88 42 f0 06 00 0d 16 98 12 89 4f ..9..9.J....[.;...../.B........O
5e60 88 49 f0 06 00 0d 14 90 72 98 52 a0 21 99 56 91 7d d1 0c 24 89 47 f0 15 0a 09 25 f4 1c 00 1d 20 .I......r.R.!.V.}..$.G....%.....
5e80 9f 49 99 49 d3 27 46 b8 2b d4 27 46 d0 1c 47 d0 08 19 d8 08 19 98 5b d1 08 28 d0 08 19 d8 08 19 .I.I.'F.+.'F..G.......[..(......
5ea0 d7 08 21 d1 08 21 a0 21 d4 08 24 d8 11 22 f2 00 02 09 25 88 41 dc 11 14 90 5b a0 35 a8 11 a1 38 ..!..!.!..$.."....%.A....[.5...8
5ec0 d1 15 2b d3 11 2c 88 42 d8 0c 13 90 72 98 52 a0 21 99 56 91 7d d1 0c 24 89 47 f0 05 02 09 25 f0 ..+..,.B....r.R.!.V.}..$.G....%.
5ee0 08 00 09 10 90 41 89 0d 88 07 d8 14 1e a0 18 d1 14 29 a8 49 d1 14 35 b8 07 d1 14 3f 88 09 d8 0b .....A...........).I..5....?....
5f00 14 90 71 8a 3d d8 1c 23 a0 69 d1 1c 2f 88 4a 90 71 8a 4d e0 1c 1d 88 4a 90 71 8a 4d f0 5d 01 2e ..q.=..#.i../.J.q.M....J.q.M.]..
5f20 05 1e f0 5e 01 00 08 0d 90 01 81 7a e0 0f 19 98 25 d1 0f 20 d0 08 20 d8 0b 15 d0 04 15 72 54 00 ...^.......z....%............rT.
5f40 00 00 63 02 00 00 00 00 00 00 00 00 00 00 00 0a 00 00 00 03 00 00 00 f3 96 00 00 00 97 00 7c 01 ..c...........................|.
5f60 7c 00 76 00 72 18 74 01 00 00 00 00 00 00 00 00 74 03 00 00 00 00 00 00 00 00 7c 00 7c 01 ab 02 |.v.r.t.........t.........|.|...
5f80 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 64 01 19 00 00 00 53 00 74 03 00 00 00 00 00 00 00 00 ..............d.....S.t.........
5fa0 7c 00 7c 01 ab 02 00 00 00 00 00 00 44 00 8f 02 8f 03 8f 04 8f 05 63 05 69 00 63 02 5d 0a 00 00 |.|.........D.........c.i.c.]...
5fc0 5c 04 00 00 7d 02 7d 03 7d 04 7d 05 7c 02 7c 05 93 02 8c 0c 04 00 63 05 7d 05 7d 04 7d 03 7d 02 \...}.}.}.}.|.|.......c.}.}.}.}.
5fe0 53 00 63 02 01 00 63 05 7d 05 7d 04 7d 03 7d 02 77 00 29 02 75 28 08 00 00 43 6f 6d 70 75 74 65 S.c...c.}.}.}.}.w.).u(...Compute
6000 20 74 68 65 20 67 65 6e 65 72 61 6c 69 7a 65 64 20 64 65 67 72 65 65 20 66 6f 72 20 6e 6f 64 65 .the.generalized.degree.for.node
6020 73 2e 0a 0a 20 20 20 20 46 6f 72 20 65 61 63 68 20 6e 6f 64 65 2c 20 74 68 65 20 67 65 6e 65 72 s.......For.each.node,.the.gener
6040 61 6c 69 7a 65 64 20 64 65 67 72 65 65 20 73 68 6f 77 73 20 68 6f 77 20 6d 61 6e 79 20 65 64 67 alized.degree.shows.how.many.edg
6060 65 73 20 6f 66 20 67 69 76 65 6e 0a 20 20 20 20 74 72 69 61 6e 67 6c 65 20 6d 75 6c 74 69 70 6c es.of.given.....triangle.multipl
6080 69 63 69 74 79 20 74 68 65 20 6e 6f 64 65 20 69 73 20 63 6f 6e 6e 65 63 74 65 64 20 74 6f 2e 20 icity.the.node.is.connected.to..
60a0 54 68 65 20 74 72 69 61 6e 67 6c 65 20 6d 75 6c 74 69 70 6c 69 63 69 74 79 0a 20 20 20 20 6f 66 The.triangle.multiplicity.....of
60c0 20 61 6e 20 65 64 67 65 20 69 73 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 74 72 69 61 6e 67 .an.edge.is.the.number.of.triang
60e0 6c 65 73 20 61 6e 20 65 64 67 65 20 70 61 72 74 69 63 69 70 61 74 65 73 20 69 6e 2e 20 54 68 65 les.an.edge.participates.in..The
6100 0a 20 20 20 20 67 65 6e 65 72 61 6c 69 7a 65 64 20 64 65 67 72 65 65 20 6f 66 20 6e 6f 64 65 20 .....generalized.degree.of.node.
6120 3a 6d 61 74 68 3a 60 69 60 20 63 61 6e 20 62 65 20 77 72 69 74 74 65 6e 20 61 73 20 61 20 76 65 :math:`i`.can.be.written.as.a.ve
6140 63 74 6f 72 0a 20 20 20 20 3a 6d 61 74 68 3a 60 5c 6d 61 74 68 62 66 7b 6b 7d 5f 69 3d 28 6b 5f ctor.....:math:`\mathbf{k}_i=(k_
6160 69 5e 7b 28 30 29 7d 2c 20 5c 64 6f 74 73 63 2c 20 6b 5f 69 5e 7b 28 4e 2d 32 29 7d 29 60 20 77 i^{(0)},.\dotsc,.k_i^{(N-2)})`.w
6180 68 65 72 65 0a 20 20 20 20 3a 6d 61 74 68 3a 60 6b 5f 69 5e 7b 28 6a 29 7d 60 20 69 73 20 74 68 here.....:math:`k_i^{(j)}`.is.th
61a0 65 20 6e 75 6d 62 65 72 20 6f 66 20 65 64 67 65 73 20 61 74 74 61 63 68 65 64 20 74 6f 20 6e 6f e.number.of.edges.attached.to.no
61c0 64 65 20 3a 6d 61 74 68 3a 60 69 60 20 74 68 61 74 0a 20 20 20 20 70 61 72 74 69 63 69 70 61 74 de.:math:`i`.that.....participat
61e0 65 20 69 6e 20 3a 6d 61 74 68 3a 60 6a 60 20 74 72 69 61 6e 67 6c 65 73 2e 0a 0a 20 20 20 20 50 e.in.:math:`j`.triangles.......P
6200 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.:
6220 20 67 72 61 70 68 0a 0a 20 20 20 20 6e 6f 64 65 73 20 3a 20 63 6f 6e 74 61 69 6e 65 72 20 6f 66 .graph......nodes.:.container.of
6240 20 6e 6f 64 65 73 2c 20 6f 70 74 69 6f 6e 61 6c 20 28 64 65 66 61 75 6c 74 3d 61 6c 6c 20 6e 6f .nodes,.optional.(default=all.no
6260 64 65 73 20 69 6e 20 47 29 0a 20 20 20 20 20 20 20 43 6f 6d 70 75 74 65 20 74 68 65 20 67 65 6e des.in.G)........Compute.the.gen
6280 65 72 61 6c 69 7a 65 64 20 64 65 67 72 65 65 20 66 6f 72 20 6e 6f 64 65 73 20 69 6e 20 74 68 69 eralized.degree.for.nodes.in.thi
62a0 73 20 63 6f 6e 74 61 69 6e 65 72 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d s.container.......Returns.....--
62c0 2d 2d 2d 2d 2d 0a 20 20 20 20 6f 75 74 20 3a 20 43 6f 75 6e 74 65 72 2c 20 6f 72 20 64 69 63 74 -----.....out.:.Counter,.or.dict
62e0 69 6f 6e 61 72 79 20 6f 66 20 43 6f 75 6e 74 65 72 73 0a 20 20 20 20 20 20 20 47 65 6e 65 72 61 ionary.of.Counters........Genera
6300 6c 69 7a 65 64 20 64 65 67 72 65 65 20 6f 66 20 73 70 65 63 69 66 69 65 64 20 6e 6f 64 65 73 2e lized.degree.of.specified.nodes.
6320 20 54 68 65 20 43 6f 75 6e 74 65 72 20 69 73 20 6b 65 79 65 64 20 62 79 20 65 64 67 65 0a 20 20 .The.Counter.is.keyed.by.edge...
6340 20 20 20 20 20 74 72 69 61 6e 67 6c 65 20 6d 75 6c 74 69 70 6c 69 63 69 74 79 2e 0a 0a 20 20 20 .....triangle.multiplicity......
6360 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 20 47 .Examples.....--------.....>>>.G
6380 20 3d 20 6e 78 2e 63 6f 6d 70 6c 65 74 65 5f 67 72 61 70 68 28 35 29 0a 20 20 20 20 3e 3e 3e 20 .=.nx.complete_graph(5).....>>>.
63a0 70 72 69 6e 74 28 6e 78 2e 67 65 6e 65 72 61 6c 69 7a 65 64 5f 64 65 67 72 65 65 28 47 2c 20 30 print(nx.generalized_degree(G,.0
63c0 29 29 0a 20 20 20 20 43 6f 75 6e 74 65 72 28 7b 33 3a 20 34 7d 29 0a 20 20 20 20 3e 3e 3e 20 70 )).....Counter({3:.4}).....>>>.p
63e0 72 69 6e 74 28 6e 78 2e 67 65 6e 65 72 61 6c 69 7a 65 64 5f 64 65 67 72 65 65 28 47 29 29 0a 20 rint(nx.generalized_degree(G))..
6400 20 20 20 7b 30 3a 20 43 6f 75 6e 74 65 72 28 7b 33 3a 20 34 7d 29 2c 20 31 3a 20 43 6f 75 6e 74 ...{0:.Counter({3:.4}),.1:.Count
6420 65 72 28 7b 33 3a 20 34 7d 29 2c 20 32 3a 20 43 6f 75 6e 74 65 72 28 7b 33 3a 20 34 7d 29 2c 20 er({3:.4}),.2:.Counter({3:.4}),.
6440 33 3a 20 43 6f 75 6e 74 65 72 28 7b 33 3a 20 34 7d 29 2c 20 34 3a 20 43 6f 75 6e 74 65 72 28 7b 3:.Counter({3:.4}),.4:.Counter({
6460 33 3a 20 34 7d 29 7d 0a 0a 20 20 20 20 54 6f 20 72 65 63 6f 76 65 72 20 74 68 65 20 6e 75 6d 62 3:.4})}......To.recover.the.numb
6480 65 72 20 6f 66 20 74 72 69 61 6e 67 6c 65 73 20 61 74 74 61 63 68 65 64 20 74 6f 20 61 20 6e 6f er.of.triangles.attached.to.a.no
64a0 64 65 3a 0a 0a 20 20 20 20 3e 3e 3e 20 6b 31 20 3d 20 6e 78 2e 67 65 6e 65 72 61 6c 69 7a 65 64 de:......>>>.k1.=.nx.generalized
64c0 5f 64 65 67 72 65 65 28 47 2c 20 30 29 0a 20 20 20 20 3e 3e 3e 20 73 75 6d 28 5b 6b 20 2a 20 76 _degree(G,.0).....>>>.sum([k.*.v
64e0 20 66 6f 72 20 6b 2c 20 76 20 69 6e 20 6b 31 2e 69 74 65 6d 73 28 29 5d 29 20 2f 20 32 20 3d 3d .for.k,.v.in.k1.items()])./.2.==
6500 20 6e 78 2e 74 72 69 61 6e 67 6c 65 73 28 47 2c 20 30 29 0a 20 20 20 20 54 72 75 65 0a 0a 20 20 .nx.triangles(G,.0).....True....
6520 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 53 65 6c 66 20 6c 6f 6f 70 73 ..Notes.....-----.....Self.loops
6540 20 61 72 65 20 69 67 6e 6f 72 65 64 2e 0a 0a 20 20 20 20 49 6e 20 61 20 6e 65 74 77 6f 72 6b 20 .are.ignored.......In.a.network.
6560 6f 66 20 4e 20 6e 6f 64 65 73 2c 20 74 68 65 20 68 69 67 68 65 73 74 20 74 72 69 61 6e 67 6c 65 of.N.nodes,.the.highest.triangle
6580 20 6d 75 6c 74 69 70 6c 69 63 69 74 79 20 61 6e 20 65 64 67 65 20 63 61 6e 20 68 61 76 65 0a 20 .multiplicity.an.edge.can.have..
65a0 20 20 20 69 73 20 4e 2d 32 2e 0a 0a 20 20 20 20 54 68 65 20 72 65 74 75 72 6e 20 76 61 6c 75 65 ...is.N-2.......The.return.value
65c0 20 64 6f 65 73 20 6e 6f 74 20 69 6e 63 6c 75 64 65 20 61 20 60 7a 65 72 6f 60 20 65 6e 74 72 79 .does.not.include.a.`zero`.entry
65e0 20 69 66 20 6e 6f 20 65 64 67 65 73 20 6f 66 20 61 0a 20 20 20 20 70 61 72 74 69 63 75 6c 61 72 .if.no.edges.of.a.....particular
6600 20 74 72 69 61 6e 67 6c 65 20 6d 75 6c 74 69 70 6c 69 63 69 74 79 20 61 72 65 20 70 72 65 73 65 .triangle.multiplicity.are.prese
6620 6e 74 2e 0a 0a 20 20 20 20 54 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 74 72 69 61 6e 67 6c 65 73 nt.......The.number.of.triangles
6640 20 6e 6f 64 65 20 3a 6d 61 74 68 3a 60 69 60 20 69 73 20 61 74 74 61 63 68 65 64 20 74 6f 20 63 .node.:math:`i`.is.attached.to.c
6660 61 6e 20 62 65 20 72 65 63 6f 76 65 72 65 64 20 66 72 6f 6d 0a 20 20 20 20 74 68 65 20 67 65 6e an.be.recovered.from.....the.gen
6680 65 72 61 6c 69 7a 65 64 20 64 65 67 72 65 65 20 3a 6d 61 74 68 3a 60 5c 6d 61 74 68 62 66 7b 6b eralized.degree.:math:`\mathbf{k
66a0 7d 5f 69 3d 28 6b 5f 69 5e 7b 28 30 29 7d 2c 20 5c 64 6f 74 73 63 2c 0a 20 20 20 20 6b 5f 69 5e }_i=(k_i^{(0)},.\dotsc,.....k_i^
66c0 7b 28 4e 2d 32 29 7d 29 60 20 62 79 20 3a 6d 61 74 68 3a 60 28 6b 5f 69 5e 7b 28 31 29 7d 2b 32 {(N-2)})`.by.:math:`(k_i^{(1)}+2
66e0 6b 5f 69 5e 7b 28 32 29 7d 2b 5c 64 6f 74 73 63 20 2b 28 4e 2d 32 29 6b 5f 69 5e 7b 28 4e 2d 32 k_i^{(2)}+\dotsc.+(N-2)k_i^{(N-2
6700 29 7d 29 2f 32 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 )})/2`.......References.....----
6720 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 4e 65 74 77 6f 72 6b 73 20 77 69 74 68 20 ------........[1].Networks.with.
6740 61 72 62 69 74 72 61 72 79 20 65 64 67 65 20 6d 75 6c 74 69 70 6c 69 63 69 74 69 65 73 20 62 79 arbitrary.edge.multiplicities.by
6760 20 56 2e 20 5a 6c 61 74 69 c4 87 2c 0a 20 20 20 20 20 20 20 20 44 2e 20 47 61 72 6c 61 73 63 68 .V..Zlati..,.........D..Garlasch
6780 65 6c 6c 69 20 61 6e 64 20 47 2e 20 43 61 6c 64 61 72 65 6c 6c 69 2c 20 45 50 4c 20 28 45 75 72 elli.and.G..Caldarelli,.EPL.(Eur
67a0 6f 70 68 79 73 69 63 73 20 4c 65 74 74 65 72 73 29 2c 0a 20 20 20 20 20 20 20 20 56 6f 6c 75 6d ophysics.Letters),.........Volum
67c0 65 20 39 37 2c 20 4e 75 6d 62 65 72 20 32 20 28 32 30 31 32 29 2e 0a 20 20 20 20 20 20 20 20 68 e.97,.Number.2.(2012)..........h
67e0 74 74 70 73 3a 2f 2f 69 6f 70 73 63 69 65 6e 63 65 2e 69 6f 70 2e 6f 72 67 2f 61 72 74 69 63 6c ttps://iopscience.iop.org/articl
6800 65 2f 31 30 2e 31 32 30 39 2f 30 32 39 35 2d 35 30 37 35 2f 39 37 2f 32 38 30 30 35 0a 20 20 20 e/10.1209/0295-5075/97/28005....
6820 20 e9 03 00 00 00 29 02 72 10 00 00 00 72 11 00 00 00 29 06 72 18 00 00 00 72 19 00 00 00 72 1a ......).r....r....).r....r....r.
6840 00 00 00 72 1b 00 00 00 72 1c 00 00 00 da 02 67 64 73 06 00 00 00 20 20 20 20 20 20 72 27 00 00 ...r....r......gds..........r'..
6860 00 72 0c 00 00 00 72 0c 00 00 00 53 02 00 00 73 4e 00 00 00 80 00 f0 7a 01 00 08 0d 90 01 81 7a .r....r....S...sN......z.......z
6880 dc 0f 13 d4 14 2e a8 71 b0 25 d3 14 38 d3 0f 39 b8 21 d1 0f 3c d0 08 3c dc 25 3f c0 01 c0 35 d3 .......q.%..8..9.!..<..<.%?...5.
68a0 25 49 d7 0b 4a d1 0b 4a 91 6b 90 61 98 11 98 41 98 72 88 41 88 72 89 45 d5 0b 4a d0 04 4a f9 d5 %I..J..J.k.a...A.r.A.r.E..J..J..
68c0 0b 4a 73 05 00 00 00 ae 0f 41 03 0a 72 2b 00 00 00 29 02 4e 72 40 00 00 00 29 03 4e 4e 54 29 02 .Js......A..r+...).Nr@...).NNT).
68e0 4e 4e 29 16 72 9a 00 00 00 da 0b 63 6f 6c 6c 65 63 74 69 6f 6e 73 72 03 00 00 00 da 09 69 74 65 NN).r......collectionsr......ite
6900 72 74 6f 6f 6c 73 72 04 00 00 00 72 05 00 00 00 da 08 6e 65 74 77 6f 72 6b 78 da 02 6e 78 da 0e rtoolsr....r......networkx..nx..
6920 6e 65 74 77 6f 72 6b 78 2e 75 74 69 6c 73 72 06 00 00 00 da 07 5f 5f 61 6c 6c 5f 5f da 0d 5f 64 networkx.utilsr......__all__.._d
6940 69 73 70 61 74 63 68 61 62 6c 65 72 07 00 00 00 72 11 00 00 00 72 65 00 00 00 72 77 00 00 00 72 ispatchabler....r....re...rw...r
6960 7c 00 00 00 72 08 00 00 00 72 09 00 00 00 72 0a 00 00 00 72 0b 00 00 00 72 0c 00 00 00 72 2c 00 |...r....r....r....r....r....r,.
6980 00 00 72 54 00 00 00 72 27 00 00 00 fa 08 3c 6d 6f 64 75 6c 65 3e 72 b4 00 00 00 01 00 00 00 73 ..rT...r'.....<module>r........s
69a0 55 01 00 00 f0 03 01 01 01 d9 00 44 e5 00 1f df 00 29 e3 00 15 dd 00 2e f2 04 07 0b 02 80 07 f1 U..........D.....)..............
69c0 14 00 02 15 90 5a d3 01 20 d8 01 03 d7 01 11 d1 01 11 f2 02 42 01 01 21 f3 03 00 02 12 f3 03 00 .....Z..............B..!........
69e0 02 21 f0 04 42 01 01 21 f1 4a 02 00 02 15 90 5c d3 01 22 f2 02 11 01 33 f3 03 00 02 23 f0 02 11 .!..B..!.J.....\.."....3....#...
6a00 01 33 f1 28 00 02 15 90 5c d3 01 22 f2 02 25 01 3d f3 03 00 02 23 f0 02 25 01 3d f1 50 01 00 02 .3.(....\.."..%.=....#..%.=.P...
6a20 15 90 5c d3 01 22 f2 02 1e 01 3e f3 03 00 02 23 f0 02 1e 01 3e f1 42 01 00 02 15 90 5c d3 01 22 ..\.."....>....#....>.B.....\.."
6a40 f2 02 3c 01 45 01 f3 03 00 02 23 f0 02 3c 01 45 01 f0 7e 01 00 02 12 80 12 d7 01 11 d1 01 11 98 ..<.E.....#..<.E..~.............
6a60 58 d4 01 26 f2 02 38 01 1b f3 03 00 02 27 f0 02 38 01 1b f0 76 01 00 02 12 80 12 d7 01 11 d1 01 X..&..8......'..8...v...........
6a80 11 98 58 d4 01 26 f2 02 6f 01 01 14 f3 03 00 02 27 f0 02 6f 01 01 14 f0 64 03 00 02 04 d7 01 11 ..X..&..o.......'..o....d.......
6aa0 d1 01 11 f1 02 27 01 37 f3 03 00 02 12 f0 02 27 01 37 f0 54 01 00 02 04 d7 01 11 d1 01 11 f2 02 .....'.7.......'.7.T............
6ac0 7b 01 01 16 f3 03 00 02 12 f0 02 7b 01 01 16 f1 7c 03 00 02 15 90 5a d3 01 20 d8 01 03 d7 01 11 {..........{....|.....Z.........
6ae0 d1 01 11 f2 02 3d 01 4b 01 f3 03 00 02 12 f3 03 00 02 21 f1 04 3d 01 4b 01 72 54 00 00 00 .....=.K..........!..=.K.rT...
generated by cgit v1.2.3 (git 2.25.1) at 2025-12-06 22:42:58 +0000