| ofs | hex dump | ascii |
|---|---|---|
| 0000 | cb 0d 0d 0a 00 00 00 00 85 fa a7 68 7c 38 00 00 e3 00 00 00 00 00 00 00 00 00 00 00 00 07 00 00 | ...........h|8.................. |
| 0020 | 00 00 00 00 00 f3 98 02 00 00 97 00 64 00 5a 00 64 01 64 02 6c 01 5a 01 64 01 64 02 6c 02 5a 03 | ............d.Z.d.d.l.Z.d.d.l.Z. |
| 0040 | 67 00 64 03 a2 01 5a 04 02 00 65 03 6a 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | g.d...Z...e.j................... |
| 0060 | 64 02 64 04 ac 05 ab 02 00 00 00 00 00 00 64 17 64 06 84 01 ab 00 00 00 00 00 00 00 5a 06 02 00 | d.d...........d.d...........Z... |
| 0080 | 65 03 6a 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 02 64 04 ac 05 ab 02 00 00 | e.j...................d.d....... |
| 00a0 | 00 00 00 00 64 17 64 07 84 01 ab 00 00 00 00 00 00 00 5a 07 02 00 65 03 6a 0a 00 00 00 00 00 00 | ....d.d...........Z...e.j....... |
| 00c0 | 00 00 00 00 00 00 00 00 00 00 00 00 64 02 64 04 ac 05 ab 02 00 00 00 00 00 00 64 17 64 08 84 01 | ............d.d...........d.d... |
| 00e0 | ab 00 00 00 00 00 00 00 5a 08 65 03 6a 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ........Z.e.j................... |
| 0100 | 6a 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 17 00 00 00 00 00 00 00 00 00 00 | j...................j........... |
| 0120 | 00 00 00 00 00 00 00 00 64 09 ab 01 00 00 00 00 00 00 02 00 65 03 6a 0a 00 00 00 00 00 00 00 00 | ........d...........e.j......... |
| 0140 | 00 00 00 00 00 00 00 00 00 00 64 02 64 04 ac 05 ab 02 00 00 00 00 00 00 64 02 64 0a 64 02 64 0b | ..........d.d...........d.d.d.d. |
| 0160 | 9c 03 64 0c 84 02 ab 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 5a 0c 65 03 6a 12 00 00 00 00 | ..d...................Z.e.j..... |
| 0180 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 1b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ..............j................. |
| 01a0 | 00 00 64 0d ab 01 00 00 00 00 00 00 65 03 6a 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ..d.........e.j................. |
| 01c0 | 00 00 6a 1b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 0e ab 01 00 00 00 00 00 00 | ..j...................d......... |
| 01e0 | 02 00 65 03 6a 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 0f 64 10 64 11 69 01 | ..e.j...................d.d.d.i. |
| 0200 | 69 01 ac 12 ab 01 00 00 00 00 00 00 64 01 64 13 9c 01 64 14 84 02 ab 00 00 00 00 00 00 00 ab 00 | i...........d.d...d............. |
| 0220 | 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 5a 0e 65 03 6a 12 00 00 00 00 00 00 00 00 00 00 00 00 | ..............Z.e.j............. |
| 0240 | 00 00 00 00 00 00 6a 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 17 00 00 00 00 | ......j...................j..... |
| 0260 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 09 ab 01 00 00 00 00 00 00 02 00 65 03 6a 0a 00 00 | ..............d...........e.j... |
| 0280 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 02 64 04 ac 05 ab 02 00 00 00 00 00 00 64 01 | ................d.d...........d. |
| 02a0 | 64 02 64 0a 64 02 64 15 9c 04 64 16 84 02 ab 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 5a 0f | d.d.d.d...d...................Z. |
| 02c0 | 79 02 29 18 7a 33 50 72 6f 76 69 64 65 73 20 65 78 70 6c 69 63 69 74 20 63 6f 6e 73 74 72 75 63 | y.).z3Provides.explicit.construc |
| 02e0 | 74 69 6f 6e 73 20 6f 66 20 65 78 70 61 6e 64 65 72 20 67 72 61 70 68 73 2e e9 00 00 00 00 4e 29 | tions.of.expander.graphs......N) |
| 0300 | 06 da 1b 6d 61 72 67 75 6c 69 73 5f 67 61 62 62 65 72 5f 67 61 6c 69 6c 5f 67 72 61 70 68 da 13 | ...margulis_gabber_galil_graph.. |
| 0320 | 63 68 6f 72 64 61 6c 5f 63 79 63 6c 65 5f 67 72 61 70 68 da 0b 70 61 6c 65 79 5f 67 72 61 70 68 | chordal_cycle_graph..paley_graph |
| 0340 | da 16 6d 61 79 62 65 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 da 13 69 73 5f 72 65 67 | ..maybe_regular_expander..is_reg |
| 0360 | 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 da 1d 72 61 6e 64 6f 6d 5f 72 65 67 75 6c 61 72 5f 65 78 | ular_expander..random_regular_ex |
| 0380 | 70 61 6e 64 65 72 5f 67 72 61 70 68 54 29 02 da 06 67 72 61 70 68 73 da 0d 72 65 74 75 72 6e 73 | pander_graphT)...graphs..returns |
| 03a0 | 5f 67 72 61 70 68 63 02 00 00 00 00 00 00 00 00 00 00 00 08 00 00 00 03 00 00 00 f3 e2 01 00 00 | _graphc......................... |
| 03c0 | 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ..t.........j................... |
| 03e0 | 64 01 7c 01 74 00 00 00 00 00 00 00 00 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | d.|.t.........j................. |
| 0400 | 00 00 ac 02 ab 03 00 00 00 00 00 00 7d 02 7c 02 6a 07 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ............}.|.j............... |
| 0420 | 00 00 00 00 ab 00 00 00 00 00 00 00 73 10 7c 02 6a 09 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ............s.|.j............... |
| 0440 | 00 00 00 00 ab 00 00 00 00 00 00 00 73 17 64 03 7d 03 74 01 00 00 00 00 00 00 00 00 6a 0a 00 00 | ............s.d.}.t.........j... |
| 0460 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 03 ab 01 00 00 00 00 00 00 82 01 74 0d 00 00 | ................|...........t... |
| 0480 | 00 00 00 00 00 00 6a 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 74 11 00 00 00 00 | ......j...................t..... |
| 04a0 | 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 64 04 ac 05 ab 02 00 00 00 00 00 00 44 00 5d 5b 00 00 | ....|.........d...........D.][.. |
| 04c0 | 5c 02 00 00 7d 04 7d 05 7c 04 64 04 7c 05 7a 05 00 00 7a 00 00 00 7c 00 7a 06 00 00 7c 05 66 02 | \...}.}.|.d.|.z...z...|.z...|.f. |
| 04e0 | 7c 04 64 04 7c 05 7a 05 00 00 64 06 7a 00 00 00 7a 00 00 00 7c 00 7a 06 00 00 7c 05 66 02 7c 04 | |.d.|.z...d.z...z...|.z...|.f.|. |
| 0500 | 7c 05 64 04 7c 04 7a 05 00 00 7a 00 00 00 7c 00 7a 06 00 00 66 02 7c 04 7c 05 64 04 7c 04 7a 05 | |.d.|.z...z...|.z...f.|.|.d.|.z. |
| 0520 | 00 00 64 06 7a 00 00 00 7a 00 00 00 7c 00 7a 06 00 00 66 02 66 04 44 00 5d 1b 00 00 5c 02 00 00 | ..d.z...z...|.z...f.f.D.]...\... |
| 0540 | 7d 06 7d 07 7c 02 6a 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 04 7c 05 66 02 | }.}.|.j...................|.|.f. |
| 0560 | 7c 06 7c 07 66 02 ab 02 00 00 00 00 00 00 01 00 8c 1d 04 00 8c 5d 04 00 64 07 7c 00 9b 00 64 08 | |.|.f................]..d.|...d. |
| 0580 | 9d 03 7c 02 6a 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 09 3c 00 00 00 7c 02 | ..|.j...................d.<...|. |
| 05a0 | 53 00 29 0a 61 d0 02 00 00 52 65 74 75 72 6e 73 20 74 68 65 20 4d 61 72 67 75 6c 69 73 2d 47 61 | S.).a....Returns.the.Margulis-Ga |
| 05c0 | 62 62 65 72 2d 47 61 6c 69 6c 20 75 6e 64 69 72 65 63 74 65 64 20 4d 75 6c 74 69 47 72 61 70 68 | bber-Galil.undirected.MultiGraph |
| 05e0 | 20 6f 6e 20 60 6e 5e 32 60 20 6e 6f 64 65 73 2e 0a 0a 20 20 20 20 54 68 65 20 75 6e 64 69 72 65 | .on.`n^2`.nodes.......The.undire |
| 0600 | 63 74 65 64 20 4d 75 6c 74 69 47 72 61 70 68 20 69 73 20 72 65 67 75 6c 61 72 20 77 69 74 68 20 | cted.MultiGraph.is.regular.with. |
| 0620 | 64 65 67 72 65 65 20 60 38 60 2e 20 4e 6f 64 65 73 20 61 72 65 20 69 6e 74 65 67 65 72 0a 20 20 | degree.`8`..Nodes.are.integer... |
| 0640 | 20 20 70 61 69 72 73 2e 20 54 68 65 20 73 65 63 6f 6e 64 2d 6c 61 72 67 65 73 74 20 65 69 67 65 | ..pairs..The.second-largest.eige |
| 0660 | 6e 76 61 6c 75 65 20 6f 66 20 74 68 65 20 61 64 6a 61 63 65 6e 63 79 20 6d 61 74 72 69 78 20 6f | nvalue.of.the.adjacency.matrix.o |
| 0680 | 66 20 74 68 65 20 67 72 61 70 68 0a 20 20 20 20 69 73 20 61 74 20 6d 6f 73 74 20 60 35 20 5c 73 | f.the.graph.....is.at.most.`5.\s |
| 06a0 | 71 72 74 7b 32 7d 60 2c 20 72 65 67 61 72 64 6c 65 73 73 20 6f 66 20 60 6e 60 2e 0a 0a 20 20 20 | qrt{2}`,.regardless.of.`n`...... |
| 06c0 | 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6e | .Parameters.....----------.....n |
| 06e0 | 20 3a 20 69 6e 74 0a 20 20 20 20 20 20 20 20 44 65 74 65 72 6d 69 6e 65 73 20 74 68 65 20 6e 75 | .:.int.........Determines.the.nu |
| 0700 | 6d 62 65 72 20 6f 66 20 6e 6f 64 65 73 20 69 6e 20 74 68 65 20 67 72 61 70 68 3a 20 60 6e 5e 32 | mber.of.nodes.in.the.graph:.`n^2 |
| 0720 | 60 2e 0a 20 20 20 20 63 72 65 61 74 65 5f 75 73 69 6e 67 20 3a 20 4e 65 74 77 6f 72 6b 58 20 67 | `......create_using.:.NetworkX.g |
| 0740 | 72 61 70 68 20 63 6f 6e 73 74 72 75 63 74 6f 72 2c 20 6f 70 74 69 6f 6e 61 6c 20 28 64 65 66 61 | raph.constructor,.optional.(defa |
| 0760 | 75 6c 74 20 4d 75 6c 74 69 47 72 61 70 68 29 0a 20 20 20 20 20 20 20 47 72 61 70 68 20 74 79 70 | ult.MultiGraph)........Graph.typ |
| 0780 | 65 20 74 6f 20 63 72 65 61 74 65 2e 20 49 66 20 67 72 61 70 68 20 69 6e 73 74 61 6e 63 65 2c 20 | e.to.create..If.graph.instance,. |
| 07a0 | 74 68 65 6e 20 63 6c 65 61 72 65 64 20 62 65 66 6f 72 65 20 70 6f 70 75 6c 61 74 65 64 2e 0a 0a | then.cleared.before.populated... |
| 07c0 | 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 47 20 3a 20 | ....Returns.....-------.....G.:. |
| 07e0 | 67 72 61 70 68 0a 20 20 20 20 20 20 20 20 54 68 65 20 63 6f 6e 73 74 72 75 63 74 65 64 20 75 6e | graph.........The.constructed.un |
| 0800 | 64 69 72 65 63 74 65 64 20 6d 75 6c 74 69 67 72 61 70 68 2e 0a 0a 20 20 20 20 52 61 69 73 65 73 | directed.multigraph.......Raises |
| 0820 | 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 4e 65 74 77 6f 72 6b 58 45 72 72 6f 72 0a 20 20 | .....------.....NetworkXError... |
| 0840 | 20 20 20 20 20 20 49 66 20 74 68 65 20 67 72 61 70 68 20 69 73 20 64 69 72 65 63 74 65 64 20 6f | ......If.the.graph.is.directed.o |
| 0860 | 72 20 6e 6f 74 20 61 20 6d 75 6c 74 69 67 72 61 70 68 2e 0a 0a 20 20 20 20 72 02 00 00 00 a9 01 | r.not.a.multigraph.......r...... |
| 0880 | da 07 64 65 66 61 75 6c 74 fa 30 60 63 72 65 61 74 65 5f 75 73 69 6e 67 60 20 6d 75 73 74 20 62 | ..default.0`create_using`.must.b |
| 08a0 | 65 20 61 6e 20 75 6e 64 69 72 65 63 74 65 64 20 6d 75 6c 74 69 67 72 61 70 68 2e e9 02 00 00 00 | e.an.undirected.multigraph...... |
| 08c0 | 29 01 da 06 72 65 70 65 61 74 e9 01 00 00 00 7a 1c 6d 61 72 67 75 6c 69 73 5f 67 61 62 62 65 72 | )...repeat.....z.margulis_gabber |
| 08e0 | 5f 67 61 6c 69 6c 5f 67 72 61 70 68 28 fa 01 29 da 04 6e 61 6d 65 29 0b da 02 6e 78 da 0b 65 6d | _galil_graph(..)..name)...nx..em |
| 0900 | 70 74 79 5f 67 72 61 70 68 da 0a 4d 75 6c 74 69 47 72 61 70 68 da 0b 69 73 5f 64 69 72 65 63 74 | pty_graph..MultiGraph..is_direct |
| 0920 | 65 64 da 0d 69 73 5f 6d 75 6c 74 69 67 72 61 70 68 da 0d 4e 65 74 77 6f 72 6b 58 45 72 72 6f 72 | ed..is_multigraph..NetworkXError |
| 0940 | da 09 69 74 65 72 74 6f 6f 6c 73 da 07 70 72 6f 64 75 63 74 da 05 72 61 6e 67 65 da 08 61 64 64 | ..itertools..product..range..add |
| 0960 | 5f 65 64 67 65 da 05 67 72 61 70 68 29 08 da 01 6e da 0c 63 72 65 61 74 65 5f 75 73 69 6e 67 da | _edge..graph)...n..create_using. |
| 0980 | 01 47 da 03 6d 73 67 da 01 78 da 01 79 da 01 75 da 01 76 73 08 00 00 00 20 20 20 20 20 20 20 20 | .G..msg..x..y..u..vs............ |
| 09a0 | fa 64 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 | .d/home/blackhao/uiuc-course-gra |
| 09c0 | 70 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 | ph/.venv/lib/python3.12/site-pac |
| 09e0 | 6b 61 67 65 73 2f 6e 65 74 77 6f 72 6b 78 2f 67 65 6e 65 72 61 74 6f 72 73 2f 65 78 70 61 6e 64 | kages/networkx/generators/expand |
| 0a00 | 65 72 73 2e 70 79 72 03 00 00 00 72 03 00 00 00 31 00 00 00 73 0a 01 00 00 80 00 f4 34 00 09 0b | ers.pyr....r....1...s.......4... |
| 0a20 | 8f 0e 89 0e 90 71 98 2c b4 02 b7 0d b1 0d d4 08 3e 80 41 d8 07 08 87 7d 81 7d 84 7f 98 61 9f 6f | .....q.,........>.A....}.}...a.o |
| 0a40 | 99 6f d4 1e 2f d8 0e 40 88 03 dc 0e 10 d7 0e 1e d1 0e 1e 98 73 d3 0e 23 d0 08 23 e4 10 19 d7 10 | .o../..@............s..#..#..... |
| 0a60 | 21 d1 10 21 a4 25 a8 01 a3 28 b0 31 d4 10 35 f2 00 07 05 27 89 04 88 01 88 31 e0 0e 0f 90 21 90 | !..!.%...(.1..5....'.....1....!. |
| 0a80 | 61 91 25 89 69 98 31 89 5f 98 61 d0 0c 20 d8 0e 0f 90 31 90 71 91 35 98 31 91 39 89 6f a0 11 d1 | a.%.i.1._.a.......1.q.5.1.9.o... |
| 0aa0 | 0d 22 a0 41 d0 0c 26 d8 0d 0e 90 11 90 51 98 11 91 55 91 19 98 61 91 0f d0 0c 20 d8 0d 0e 90 11 | .".A..&......Q...U...a.......... |
| 0ac0 | 90 61 98 21 91 65 98 61 91 69 91 1f a0 41 d1 10 25 d0 0c 26 f0 09 05 15 0a f2 00 06 09 27 89 44 | .a.!.e.a.i...A..%..&.........'.D |
| 0ae0 | 88 41 88 71 f0 0c 00 0d 0e 8f 4a 89 4a 98 01 98 31 90 76 a0 01 a0 31 98 76 d5 0c 26 f1 0d 06 09 | .A.q......J.J...1.v...1.v..&.... |
| 0b00 | 27 f0 03 07 05 27 f0 10 00 19 35 b0 51 b0 43 b0 71 d0 16 39 80 41 87 47 81 47 88 46 81 4f d8 0b | '....'....5.Q.C.q..9.A.G.G.F.O.. |
| 0b20 | 0c 80 48 f3 00 00 00 00 63 02 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 03 00 00 00 f3 8c 01 | ..H.....c....................... |
| 0b40 | 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ....t.........j................. |
| 0b60 | 00 00 64 01 7c 01 74 00 00 00 00 00 00 00 00 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ..d.|.t.........j............... |
| 0b80 | 00 00 00 00 ac 02 ab 03 00 00 00 00 00 00 7d 02 7c 02 6a 07 00 00 00 00 00 00 00 00 00 00 00 00 | ..............}.|.j............. |
| 0ba0 | 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 73 10 7c 02 6a 09 00 00 00 00 00 00 00 00 00 00 00 00 | ..............s.|.j............. |
| 0bc0 | 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 73 17 64 03 7d 03 74 01 00 00 00 00 00 00 00 00 6a 0a | ..............s.d.}.t.........j. |
| 0be0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 03 ab 01 00 00 00 00 00 00 82 01 74 0d | ..................|...........t. |
| 0c00 | 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 44 00 5d 45 00 00 7d 04 7c 04 64 04 7a 0a | ........|.........D.]E..}.|.d.z. |
| 0c20 | 00 00 7c 00 7a 06 00 00 7d 05 7c 04 64 04 7a 00 00 00 7c 00 7a 06 00 00 7d 06 7c 04 64 01 6b 44 | ..|.z...}.|.d.z...|.z...}.|.d.kD |
| 0c40 | 00 00 72 10 74 0f 00 00 00 00 00 00 00 00 7c 04 7c 00 64 05 7a 0a 00 00 7c 00 ab 03 00 00 00 00 | ..r.t.........|.|.d.z...|....... |
| 0c60 | 00 00 6e 01 64 01 7d 07 7c 05 7c 06 7c 07 66 03 44 00 5d 14 00 00 7d 08 7c 02 6a 11 00 00 00 00 | ..n.d.}.|.|.|.f.D.]...}.|.j..... |
| 0c80 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 04 7c 08 ab 02 00 00 00 00 00 00 01 00 8c 16 04 00 | ..............|.|............... |
| 0ca0 | 8c 47 04 00 64 06 7c 00 9b 00 64 07 9d 03 7c 02 6a 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | .G..d.|...d...|.j............... |
| 0cc0 | 00 00 00 00 64 08 3c 00 00 00 7c 02 53 00 29 09 75 04 04 00 00 52 65 74 75 72 6e 73 20 74 68 65 | ....d.<...|.S.).u....Returns.the |
| 0ce0 | 20 63 68 6f 72 64 61 6c 20 63 79 63 6c 65 20 67 72 61 70 68 20 6f 6e 20 60 70 60 20 6e 6f 64 65 | .chordal.cycle.graph.on.`p`.node |
| 0d00 | 73 2e 0a 0a 20 20 20 20 54 68 65 20 72 65 74 75 72 6e 65 64 20 67 72 61 70 68 20 69 73 20 61 20 | s.......The.returned.graph.is.a. |
| 0d20 | 63 79 63 6c 65 20 67 72 61 70 68 20 6f 6e 20 60 70 60 20 6e 6f 64 65 73 20 77 69 74 68 20 63 68 | cycle.graph.on.`p`.nodes.with.ch |
| 0d40 | 6f 72 64 73 20 6a 6f 69 6e 69 6e 67 20 65 61 63 68 0a 20 20 20 20 76 65 72 74 65 78 20 60 78 60 | ords.joining.each.....vertex.`x` |
| 0d60 | 20 74 6f 20 69 74 73 20 69 6e 76 65 72 73 65 20 6d 6f 64 75 6c 6f 20 60 70 60 2e 20 54 68 69 73 | .to.its.inverse.modulo.`p`..This |
| 0d80 | 20 67 72 61 70 68 20 69 73 20 61 20 28 6d 69 6c 64 6c 79 20 65 78 70 6c 69 63 69 74 29 0a 20 20 | .graph.is.a.(mildly.explicit)... |
| 0da0 | 20 20 33 2d 72 65 67 75 6c 61 72 20 65 78 70 61 6e 64 65 72 20 5b 31 5d 5f 2e 0a 0a 20 20 20 20 | ..3-regular.expander.[1]_....... |
| 0dc0 | 60 70 60 20 2a 6d 75 73 74 2a 20 62 65 20 61 20 70 72 69 6d 65 20 6e 75 6d 62 65 72 2e 0a 0a 20 | `p`.*must*.be.a.prime.number.... |
| 0de0 | 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 2d 2d 0a 20 20 20 | ...Parameters.....----------.... |
| 0e00 | 20 70 20 3a 20 61 20 70 72 69 6d 65 20 6e 75 6d 62 65 72 0a 0a 20 20 20 20 20 20 20 20 54 68 65 | .p.:.a.prime.number..........The |
| 0e20 | 20 6e 75 6d 62 65 72 20 6f 66 20 76 65 72 74 69 63 65 73 20 69 6e 20 74 68 65 20 67 72 61 70 68 | .number.of.vertices.in.the.graph |
| 0e40 | 2e 20 54 68 69 73 20 61 6c 73 6f 20 69 6e 64 69 63 61 74 65 73 20 77 68 65 72 65 20 74 68 65 0a | ..This.also.indicates.where.the. |
| 0e60 | 20 20 20 20 20 20 20 20 63 68 6f 72 64 61 6c 20 65 64 67 65 73 20 69 6e 20 74 68 65 20 63 79 63 | ........chordal.edges.in.the.cyc |
| 0e80 | 6c 65 20 77 69 6c 6c 20 62 65 20 63 72 65 61 74 65 64 2e 0a 0a 20 20 20 20 63 72 65 61 74 65 5f | le.will.be.created.......create_ |
| 0ea0 | 75 73 69 6e 67 20 3a 20 4e 65 74 77 6f 72 6b 58 20 67 72 61 70 68 20 63 6f 6e 73 74 72 75 63 74 | using.:.NetworkX.graph.construct |
| 0ec0 | 6f 72 2c 20 6f 70 74 69 6f 6e 61 6c 20 28 64 65 66 61 75 6c 74 3d 6e 78 2e 47 72 61 70 68 29 0a | or,.optional.(default=nx.Graph). |
| 0ee0 | 20 20 20 20 20 20 20 47 72 61 70 68 20 74 79 70 65 20 74 6f 20 63 72 65 61 74 65 2e 20 49 66 20 | .......Graph.type.to.create..If. |
| 0f00 | 67 72 61 70 68 20 69 6e 73 74 61 6e 63 65 2c 20 74 68 65 6e 20 63 6c 65 61 72 65 64 20 62 65 66 | graph.instance,.then.cleared.bef |
| 0f20 | 6f 72 65 20 70 6f 70 75 6c 61 74 65 64 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 | ore.populated.......Returns..... |
| 0f40 | 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 20 20 20 20 54 68 | -------.....G.:.graph.........Th |
| 0f60 | 65 20 63 6f 6e 73 74 72 75 63 74 65 64 20 75 6e 64 69 72 65 63 74 65 64 20 6d 75 6c 74 69 67 72 | e.constructed.undirected.multigr |
| 0f80 | 61 70 68 2e 0a 0a 20 20 20 20 52 61 69 73 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 | aph.......Raises.....------..... |
| 0fa0 | 4e 65 74 77 6f 72 6b 58 45 72 72 6f 72 0a 0a 20 20 20 20 20 20 20 20 49 66 20 60 63 72 65 61 74 | NetworkXError..........If.`creat |
| 0fc0 | 65 5f 75 73 69 6e 67 60 20 69 6e 64 69 63 61 74 65 73 20 64 69 72 65 63 74 65 64 20 6f 72 20 6e | e_using`.indicates.directed.or.n |
| 0fe0 | 6f 74 20 61 20 6d 75 6c 74 69 67 72 61 70 68 2e 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 | ot.a.multigraph.......References |
| 1000 | 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 54 68 65 6f | .....----------.........[1].Theo |
| 1020 | 72 65 6d 20 34 2e 34 2e 32 20 69 6e 20 41 2e 20 4c 75 62 6f 74 7a 6b 79 2e 20 22 44 69 73 63 72 | rem.4.4.2.in.A..Lubotzky.."Discr |
| 1040 | 65 74 65 20 67 72 6f 75 70 73 2c 20 65 78 70 61 6e 64 69 6e 67 20 67 72 61 70 68 73 20 61 6e 64 | ete.groups,.expanding.graphs.and |
| 1060 | 0a 20 20 20 20 20 20 20 20 20 20 20 69 6e 76 61 72 69 61 6e 74 20 6d 65 61 73 75 72 65 73 22 2c | ............invariant.measures", |
| 1080 | 20 76 6f 6c 75 6d 65 20 31 32 35 20 6f 66 20 50 72 6f 67 72 65 73 73 20 69 6e 20 4d 61 74 68 65 | .volume.125.of.Progress.in.Mathe |
| 10a0 | 6d 61 74 69 63 73 2e 0a 20 20 20 20 20 20 20 20 20 20 20 42 69 72 6b 68 c3 a4 75 73 65 72 20 56 | matics.............Birkh..user.V |
| 10c0 | 65 72 6c 61 67 2c 20 42 61 73 65 6c 2c 20 31 39 39 34 2e 0a 0a 20 20 20 20 72 02 00 00 00 72 0c | erlag,.Basel,.1994.......r....r. |
| 10e0 | 00 00 00 72 0e 00 00 00 72 11 00 00 00 72 0f 00 00 00 7a 14 63 68 6f 72 64 61 6c 5f 63 79 63 6c | ...r....r....r....z.chordal_cycl |
| 1100 | 65 5f 67 72 61 70 68 28 72 12 00 00 00 72 13 00 00 00 29 0a 72 14 00 00 00 72 15 00 00 00 72 16 | e_graph(r....r....).r....r....r. |
| 1120 | 00 00 00 72 17 00 00 00 72 18 00 00 00 72 19 00 00 00 72 1c 00 00 00 da 03 70 6f 77 72 1d 00 00 | ...r....r....r....r......powr... |
| 1140 | 00 72 1e 00 00 00 29 09 da 01 70 72 20 00 00 00 72 21 00 00 00 72 22 00 00 00 72 23 00 00 00 da | .r....)...pr....r!...r"...r#.... |
| 1160 | 04 6c 65 66 74 da 05 72 69 67 68 74 da 05 63 68 6f 72 64 72 24 00 00 00 73 09 00 00 00 20 20 20 | .left..right..chordr$...s....... |
| 1180 | 20 20 20 20 20 20 72 27 00 00 00 72 04 00 00 00 72 04 00 00 00 5c 00 00 00 73 cd 00 00 00 80 00 | ......r'...r....r....\...s...... |
| 11a0 | f4 4e 01 00 09 0b 8f 0e 89 0e 90 71 98 2c b4 02 b7 0d b1 0d d4 08 3e 80 41 d8 07 08 87 7d 81 7d | .N.........q.,........>.A....}.} |
| 11c0 | 84 7f 98 61 9f 6f 99 6f d4 1e 2f d8 0e 40 88 03 dc 0e 10 d7 0e 1e d1 0e 1e 98 73 d3 0e 23 d0 08 | ...a.o.o../..@............s..#.. |
| 11e0 | 23 e4 0d 12 90 31 8b 58 f2 00 0f 05 1d 88 01 d8 10 11 90 41 91 05 98 11 89 7b 88 04 d8 11 12 90 | #....1.X...........A.....{...... |
| 1200 | 51 91 15 98 21 91 0b 88 05 f0 16 00 25 26 a8 01 a2 45 94 03 90 41 90 71 98 31 91 75 98 61 d4 10 | Q...!.......%&...E...A.q.1.u.a.. |
| 1220 | 20 a8 71 88 05 d8 12 16 98 05 98 75 d0 11 25 f2 00 01 09 1d 88 41 d8 0c 0d 8f 4a 89 4a 90 71 98 | ..q........u..%......A....J.J.q. |
| 1240 | 21 d5 0c 1c f1 03 01 09 1d f0 1d 0f 05 1d f0 20 00 19 2d a8 51 a8 43 a8 71 d0 16 31 80 41 87 47 | !.................-.Q.C.q..1.A.G |
| 1260 | 81 47 88 46 81 4f d8 0b 0c 80 48 72 28 00 00 00 63 02 00 00 00 00 00 00 00 00 00 00 00 07 00 00 | .G.F.O....Hr(...c............... |
| 1280 | 00 03 00 00 00 f3 84 01 00 00 97 00 74 01 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 | ............t.........j......... |
| 12a0 | 00 00 00 00 00 00 00 00 00 00 64 01 7c 01 74 00 00 00 00 00 00 00 00 00 6a 04 00 00 00 00 00 00 | ..........d.|.t.........j....... |
| 12c0 | 00 00 00 00 00 00 00 00 00 00 00 00 ac 02 ab 03 00 00 00 00 00 00 7d 02 7c 02 6a 07 00 00 00 00 | ......................}.|.j..... |
| 12e0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 72 17 64 03 7d 03 74 01 00 00 | ......................r.d.}.t... |
| 1300 | 00 00 00 00 00 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 03 ab 01 00 00 | ......j...................|..... |
| 1320 | 00 00 00 00 82 01 74 0b 00 00 00 00 00 00 00 00 64 04 7c 00 ab 02 00 00 00 00 00 00 44 00 8f 04 | ......t.........d.|.........D... |
| 1340 | 63 02 68 00 63 02 5d 16 00 00 7d 04 7c 04 64 05 7a 08 00 00 7c 00 7a 06 00 00 64 01 6b 37 00 00 | c.h.c.]...}.|.d.z...|.z...d.k7.. |
| 1360 | 73 01 8c 0f 7c 04 64 05 7a 08 00 00 7c 00 7a 06 00 00 92 02 8c 18 04 00 7d 05 7d 04 74 0b 00 00 | s...|.d.z...|.z.........}.}.t... |
| 1380 | 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 44 00 5d 21 00 00 7d 04 7c 05 44 00 5d 1a 00 00 | ......|.........D.]!..}.|.D.]... |
| 13a0 | 7d 06 7c 02 6a 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 04 7c 04 7c 06 7a 00 | }.|.j...................|.|.|.z. |
| 13c0 | 00 00 7c 00 7a 06 00 00 ab 02 00 00 00 00 00 00 01 00 8c 1c 04 00 8c 23 04 00 64 06 7c 00 9b 00 | ..|.z..................#..d.|... |
| 13e0 | 64 07 9d 03 7c 02 6a 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 08 3c 00 00 00 | d...|.j...................d.<... |
| 1400 | 7c 02 53 00 63 02 01 00 63 02 7d 04 77 00 29 09 61 2d 06 00 00 52 65 74 75 72 6e 73 20 74 68 65 | |.S.c...c.}.w.).a-...Returns.the |
| 1420 | 20 50 61 6c 65 79 20 24 5c 66 72 61 63 7b 28 70 2d 31 29 7d 7b 32 7d 24 20 2d 72 65 67 75 6c 61 | .Paley.$\frac{(p-1)}{2}$.-regula |
| 1440 | 72 20 67 72 61 70 68 20 6f 6e 20 24 70 24 20 6e 6f 64 65 73 2e 0a 0a 20 20 20 20 54 68 65 20 72 | r.graph.on.$p$.nodes.......The.r |
| 1460 | 65 74 75 72 6e 65 64 20 67 72 61 70 68 20 69 73 20 61 20 67 72 61 70 68 20 6f 6e 20 24 5c 6d 61 | eturned.graph.is.a.graph.on.$\ma |
| 1480 | 74 68 62 62 7b 5a 7d 2f 70 5c 6d 61 74 68 62 62 7b 5a 7d 24 20 77 69 74 68 20 65 64 67 65 73 20 | thbb{Z}/p\mathbb{Z}$.with.edges. |
| 14a0 | 62 65 74 77 65 65 6e 20 24 78 24 20 61 6e 64 20 24 79 24 0a 20 20 20 20 69 66 20 61 6e 64 20 6f | between.$x$.and.$y$.....if.and.o |
| 14c0 | 6e 6c 79 20 69 66 20 24 78 2d 79 24 20 69 73 20 61 20 6e 6f 6e 7a 65 72 6f 20 73 71 75 61 72 65 | nly.if.$x-y$.is.a.nonzero.square |
| 14e0 | 20 69 6e 20 24 5c 6d 61 74 68 62 62 7b 5a 7d 2f 70 5c 6d 61 74 68 62 62 7b 5a 7d 24 2e 0a 0a 20 | .in.$\mathbb{Z}/p\mathbb{Z}$.... |
| 1500 | 20 20 20 49 66 20 24 70 20 5c 65 71 75 69 76 20 31 20 20 5c 70 6d 6f 64 20 34 24 2c 20 24 2d 31 | ...If.$p.\equiv.1..\pmod.4$,.$-1 |
| 1520 | 24 20 69 73 20 61 20 73 71 75 61 72 65 20 69 6e 0a 20 20 20 20 24 5c 6d 61 74 68 62 62 7b 5a 7d | $.is.a.square.in.....$\mathbb{Z} |
| 1540 | 2f 70 5c 6d 61 74 68 62 62 7b 5a 7d 24 20 61 6e 64 20 74 68 65 72 65 66 6f 72 65 20 24 78 2d 79 | /p\mathbb{Z}$.and.therefore.$x-y |
| 1560 | 24 20 69 73 20 61 20 73 71 75 61 72 65 20 69 66 20 61 6e 64 0a 20 20 20 20 6f 6e 6c 79 20 69 66 | $.is.a.square.if.and.....only.if |
| 1580 | 20 24 79 2d 78 24 20 69 73 20 61 6c 73 6f 20 61 20 73 71 75 61 72 65 2c 20 69 2e 65 20 74 68 65 | .$y-x$.is.also.a.square,.i.e.the |
| 15a0 | 20 65 64 67 65 73 20 69 6e 20 74 68 65 20 50 61 6c 65 79 20 67 72 61 70 68 20 61 72 65 20 73 79 | .edges.in.the.Paley.graph.are.sy |
| 15c0 | 6d 6d 65 74 72 69 63 2e 0a 0a 20 20 20 20 49 66 20 24 70 20 5c 65 71 75 69 76 20 33 20 5c 70 6d | mmetric.......If.$p.\equiv.3.\pm |
| 15e0 | 6f 64 20 34 24 2c 20 24 2d 31 24 20 69 73 20 6e 6f 74 20 61 20 73 71 75 61 72 65 20 69 6e 20 24 | od.4$,.$-1$.is.not.a.square.in.$ |
| 1600 | 5c 6d 61 74 68 62 62 7b 5a 7d 2f 70 5c 6d 61 74 68 62 62 7b 5a 7d 24 0a 20 20 20 20 61 6e 64 20 | \mathbb{Z}/p\mathbb{Z}$.....and. |
| 1620 | 74 68 65 72 65 66 6f 72 65 20 65 69 74 68 65 72 20 24 78 2d 79 24 20 6f 72 20 24 79 2d 78 24 20 | therefore.either.$x-y$.or.$y-x$. |
| 1640 | 69 73 20 61 20 73 71 75 61 72 65 20 69 6e 20 24 5c 6d 61 74 68 62 62 7b 5a 7d 2f 70 5c 6d 61 74 | is.a.square.in.$\mathbb{Z}/p\mat |
| 1660 | 68 62 62 7b 5a 7d 24 20 62 75 74 20 6e 6f 74 20 62 6f 74 68 2e 0a 0a 20 20 20 20 4e 6f 74 65 20 | hbb{Z}$.but.not.both.......Note. |
| 1680 | 74 68 61 74 20 61 20 6d 6f 72 65 20 67 65 6e 65 72 61 6c 20 64 65 66 69 6e 69 74 69 6f 6e 20 6f | that.a.more.general.definition.o |
| 16a0 | 66 20 50 61 6c 65 79 20 67 72 61 70 68 73 20 65 78 74 65 6e 64 73 20 74 68 69 73 20 63 6f 6e 73 | f.Paley.graphs.extends.this.cons |
| 16c0 | 74 72 75 63 74 69 6f 6e 0a 20 20 20 20 74 6f 20 67 72 61 70 68 73 20 6f 76 65 72 20 24 71 3d 70 | truction.....to.graphs.over.$q=p |
| 16e0 | 5e 6e 24 20 76 65 72 74 69 63 65 73 2c 20 62 79 20 75 73 69 6e 67 20 74 68 65 20 66 69 6e 69 74 | ^n$.vertices,.by.using.the.finit |
| 1700 | 65 20 66 69 65 6c 64 20 24 46 5f 71 24 20 69 6e 73 74 65 61 64 20 6f 66 0a 20 20 20 20 24 5c 6d | e.field.$F_q$.instead.of.....$\m |
| 1720 | 61 74 68 62 62 7b 5a 7d 2f 70 5c 6d 61 74 68 62 62 7b 5a 7d 24 2e 0a 20 20 20 20 54 68 69 73 20 | athbb{Z}/p\mathbb{Z}$......This. |
| 1740 | 63 6f 6e 73 74 72 75 63 74 69 6f 6e 20 72 65 71 75 69 72 65 73 20 74 6f 20 63 6f 6d 70 75 74 65 | construction.requires.to.compute |
| 1760 | 20 73 71 75 61 72 65 73 20 69 6e 20 67 65 6e 65 72 61 6c 20 66 69 6e 69 74 65 20 66 69 65 6c 64 | .squares.in.general.finite.field |
| 1780 | 73 20 61 6e 64 20 69 73 0a 20 20 20 20 6e 6f 74 20 77 68 61 74 20 69 73 20 69 6d 70 6c 65 6d 65 | s.and.is.....not.what.is.impleme |
| 17a0 | 6e 74 65 64 20 68 65 72 65 20 28 69 2e 65 20 60 70 61 6c 65 79 5f 67 72 61 70 68 28 32 35 29 60 | nted.here.(i.e.`paley_graph(25)` |
| 17c0 | 20 64 6f 65 73 20 6e 6f 74 20 72 65 74 75 72 6e 20 74 68 65 20 74 72 75 65 0a 20 20 20 20 50 61 | .does.not.return.the.true.....Pa |
| 17e0 | 6c 65 79 20 67 72 61 70 68 20 61 73 73 6f 63 69 61 74 65 64 20 77 69 74 68 20 24 35 5e 32 24 29 | ley.graph.associated.with.$5^2$) |
| 1800 | 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d | .......Parameters.....---------- |
| 1820 | 0a 20 20 20 20 70 20 3a 20 69 6e 74 2c 20 61 6e 20 6f 64 64 20 70 72 69 6d 65 20 6e 75 6d 62 65 | .....p.:.int,.an.odd.prime.numbe |
| 1840 | 72 2e 0a 0a 20 20 20 20 63 72 65 61 74 65 5f 75 73 69 6e 67 20 3a 20 4e 65 74 77 6f 72 6b 58 20 | r.......create_using.:.NetworkX. |
| 1860 | 67 72 61 70 68 20 63 6f 6e 73 74 72 75 63 74 6f 72 2c 20 6f 70 74 69 6f 6e 61 6c 20 28 64 65 66 | graph.constructor,.optional.(def |
| 1880 | 61 75 6c 74 3d 6e 78 2e 47 72 61 70 68 29 0a 20 20 20 20 20 20 20 47 72 61 70 68 20 74 79 70 65 | ault=nx.Graph)........Graph.type |
| 18a0 | 20 74 6f 20 63 72 65 61 74 65 2e 20 49 66 20 67 72 61 70 68 20 69 6e 73 74 61 6e 63 65 2c 20 74 | .to.create..If.graph.instance,.t |
| 18c0 | 68 65 6e 20 63 6c 65 61 72 65 64 20 62 65 66 6f 72 65 20 70 6f 70 75 6c 61 74 65 64 2e 0a 0a 20 | hen.cleared.before.populated.... |
| 18e0 | 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 47 20 3a 20 67 | ...Returns.....-------.....G.:.g |
| 1900 | 72 61 70 68 0a 20 20 20 20 20 20 20 20 54 68 65 20 63 6f 6e 73 74 72 75 63 74 65 64 20 64 69 72 | raph.........The.constructed.dir |
| 1920 | 65 63 74 65 64 20 67 72 61 70 68 2e 0a 0a 20 20 20 20 52 61 69 73 65 73 0a 20 20 20 20 2d 2d 2d | ected.graph.......Raises.....--- |
| 1940 | 2d 2d 2d 0a 20 20 20 20 4e 65 74 77 6f 72 6b 58 45 72 72 6f 72 0a 20 20 20 20 20 20 20 20 49 66 | ---.....NetworkXError.........If |
| 1960 | 20 74 68 65 20 67 72 61 70 68 20 69 73 20 61 20 6d 75 6c 74 69 67 72 61 70 68 2e 0a 0a 20 20 20 | .the.graph.is.a.multigraph...... |
| 1980 | 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 43 | .References.....----------.....C |
| 19a0 | 68 61 70 74 65 72 20 31 33 20 69 6e 20 42 2e 20 42 6f 6c 6c 6f 62 61 73 2c 20 52 61 6e 64 6f 6d | hapter.13.in.B..Bollobas,.Random |
| 19c0 | 20 47 72 61 70 68 73 2e 20 53 65 63 6f 6e 64 20 65 64 69 74 69 6f 6e 2e 0a 20 20 20 20 43 61 6d | .Graphs..Second.edition......Cam |
| 19e0 | 62 72 69 64 67 65 20 53 74 75 64 69 65 73 20 69 6e 20 41 64 76 61 6e 63 65 64 20 4d 61 74 68 65 | bridge.Studies.in.Advanced.Mathe |
| 1a00 | 6d 61 74 69 63 73 2c 20 37 33 2e 0a 20 20 20 20 43 61 6d 62 72 69 64 67 65 20 55 6e 69 76 65 72 | matics,.73......Cambridge.Univer |
| 1a20 | 73 69 74 79 20 50 72 65 73 73 2c 20 43 61 6d 62 72 69 64 67 65 20 28 32 30 30 31 29 2e 0a 20 20 | sity.Press,.Cambridge.(2001).... |
| 1a40 | 20 20 72 02 00 00 00 72 0c 00 00 00 7a 26 60 63 72 65 61 74 65 5f 75 73 69 6e 67 60 20 63 61 6e | ..r....r....z&`create_using`.can |
| 1a60 | 6e 6f 74 20 62 65 20 61 20 6d 75 6c 74 69 67 72 61 70 68 2e 72 11 00 00 00 72 0f 00 00 00 7a 06 | not.be.a.multigraph.r....r....z. |
| 1a80 | 70 61 6c 65 79 28 72 12 00 00 00 72 13 00 00 00 29 08 72 14 00 00 00 72 15 00 00 00 da 07 44 69 | paley(r....r....).r....r......Di |
| 1aa0 | 47 72 61 70 68 72 18 00 00 00 72 19 00 00 00 72 1c 00 00 00 72 1d 00 00 00 72 1e 00 00 00 29 07 | Graphr....r....r....r....r....). |
| 1ac0 | 72 2b 00 00 00 72 20 00 00 00 72 21 00 00 00 72 22 00 00 00 72 23 00 00 00 da 0a 73 71 75 61 72 | r+...r....r!...r"...r#.....squar |
| 1ae0 | 65 5f 73 65 74 da 02 78 32 73 07 00 00 00 20 20 20 20 20 20 20 72 27 00 00 00 72 05 00 00 00 72 | e_set..x2s...........r'...r....r |
| 1b00 | 05 00 00 00 9c 00 00 00 73 c6 00 00 00 80 00 f4 58 01 00 09 0b 8f 0e 89 0e 90 71 98 2c b4 02 b7 | ........s.......X.........q.,... |
| 1b20 | 0a b1 0a d4 08 3b 80 41 d8 07 08 87 7f 81 7f d4 07 18 d8 0e 36 88 03 dc 0e 10 d7 0e 1e d1 0e 1e | .....;.A............6........... |
| 1b40 | 98 73 d3 0e 23 d0 08 23 f4 0a 00 27 2c a8 41 a8 71 a3 6b d6 11 45 a0 11 b0 61 b8 11 b1 64 b8 61 | .s..#..#...',.A.q.k..E...a...d.a |
| 1b60 | b1 5a c0 31 b3 5f 90 31 90 61 91 34 98 31 93 2a d0 11 45 80 4a d0 11 45 e4 0d 12 90 31 8b 58 f2 | .Z.1._.1.a.4.1.*..E.J..E....1.X. |
| 1b80 | 00 02 05 28 88 01 d8 12 1c f2 00 01 09 28 88 42 d8 0c 0d 8f 4a 89 4a 90 71 98 31 98 72 99 36 a0 | ...(.........(.B....J.J.q.1.r.6. |
| 1ba0 | 51 99 2c d5 0c 27 f1 03 01 09 28 f0 03 02 05 28 f0 06 00 19 1f 98 71 98 63 a0 11 90 6d 80 41 87 | Q.,..'....(....(......q.c...m.A. |
| 1bc0 | 47 81 47 88 46 81 4f d8 0b 0c 80 48 f9 f2 0d 00 12 46 01 73 0c 00 00 00 c1 1c 10 42 3d 04 c1 2d | G.G.F.O....H.....F.s.......B=..- |
| 1be0 | 0a 42 3d 04 da 04 73 65 65 64 e9 64 00 00 00 a9 03 72 20 00 00 00 da 09 6d 61 78 5f 74 72 69 65 | .B=...seed.d.....r......max_trie |
| 1c00 | 73 72 33 00 00 00 63 02 00 00 00 00 00 00 00 03 00 00 00 07 00 00 00 03 00 00 00 f3 88 03 00 00 | sr3...c......................... |
| 1c20 | 97 00 64 01 64 02 6c 00 7d 05 7c 00 64 03 6b 02 00 00 72 15 74 03 00 00 00 00 00 00 00 00 6a 04 | ..d.d.l.}.|.d.k...r.t.........j. |
| 1c40 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 04 ab 01 00 00 00 00 00 00 82 01 7c 01 | ..................d...........|. |
| 1c60 | 64 05 6b 5c 00 00 73 15 74 03 00 00 00 00 00 00 00 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 | d.k\..s.t.........j............. |
| 1c80 | 00 00 00 00 00 00 64 06 ab 01 00 00 00 00 00 00 82 01 7c 01 64 05 7a 06 00 00 64 01 6b 28 00 00 | ......d...........|.d.z...d.k(.. |
| 1ca0 | 73 15 74 03 00 00 00 00 00 00 00 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | s.t.........j................... |
| 1cc0 | 64 07 ab 01 00 00 00 00 00 00 82 01 7c 00 64 03 7a 0a 00 00 7c 01 6b 5c 00 00 73 1f 74 03 00 00 | d...........|.d.z...|.k\..s.t... |
| 1ce0 | 00 00 00 00 00 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 08 7c 01 64 05 | ......j...................d.|.d. |
| 1d00 | 7a 02 00 00 9b 00 64 09 7c 00 9b 00 64 0a 9d 05 ab 01 00 00 00 00 00 00 82 01 74 03 00 00 00 00 | z.....d.|...d.............t..... |
| 1d20 | 00 00 00 00 6a 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 7c 02 ab 02 00 00 | ....j...................|.|..... |
| 1d40 | 00 00 00 00 7d 06 7c 00 64 05 6b 02 00 00 72 02 7c 06 53 00 67 00 7d 07 74 09 00 00 00 00 00 00 | ....}.|.d.k...r.|.S.g.}.t....... |
| 1d60 | 00 00 ab 00 00 00 00 00 00 00 7d 08 74 0b 00 00 00 00 00 00 00 00 7c 01 64 05 7a 02 00 00 ab 01 | ..........}.t.........|.d.z..... |
| 1d80 | 00 00 00 00 00 00 44 00 5d f4 00 00 7d 09 7c 03 7d 0a 74 0d 00 00 00 00 00 00 00 00 7c 08 ab 01 | ......D.]...}.|.}.t.........|... |
| 1da0 | 00 00 00 00 00 00 7c 09 64 03 7a 00 00 00 7c 00 7a 05 00 00 6b 37 00 00 73 01 8c 1a 7c 0a 64 03 | ......|.d.z...|.z...k7..s...|.d. |
| 1dc0 | 7a 17 00 00 7d 0a 7c 04 6a 0f 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 64 03 | z...}.|.j...................|.d. |
| 1de0 | 7a 0a 00 00 ab 01 00 00 00 00 00 00 6a 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | z...........j................... |
| 1e00 | ab 00 00 00 00 00 00 00 7d 0b 7c 0b 6a 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ........}.|.j................... |
| 1e20 | 7c 00 64 03 7a 0a 00 00 ab 01 00 00 00 00 00 00 01 00 74 02 00 00 00 00 00 00 00 00 6a 14 00 00 | |.d.z.............t.........j... |
| 1e40 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 17 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ................j............... |
| 1e60 | 00 00 00 00 7c 0b 64 0b ac 0c ab 02 00 00 00 00 00 00 44 00 8f 0c 8f 0d 63 03 68 00 63 02 5d 15 | ....|.d...........D.....c.h.c.]. |
| 1e80 | 00 00 5c 02 00 00 7d 0c 7d 0d 7c 0c 7c 0d 66 02 7c 08 76 01 72 0a 7c 0d 7c 0c 66 02 7c 08 76 01 | ..\...}.}.|.|.f.|.v.r.|.|.f.|.v. |
| 1ea0 | 72 04 7c 0c 7c 0d 66 02 92 02 8c 17 04 00 7d 0e 7d 0c 7d 0d 74 0d 00 00 00 00 00 00 00 00 7c 0e | r.|.|.f.......}.}.}.t.........|. |
| 1ec0 | ab 01 00 00 00 00 00 00 7c 00 6b 28 00 00 72 22 7c 07 6a 13 00 00 00 00 00 00 00 00 00 00 00 00 | ........|.k(..r"|.j............. |
| 1ee0 | 00 00 00 00 00 00 7c 0b ab 01 00 00 00 00 00 00 01 00 7c 08 6a 19 00 00 00 00 00 00 00 00 00 00 | ......|...........|.j........... |
| 1f00 | 00 00 00 00 00 00 00 00 7c 0e ab 01 00 00 00 00 00 00 01 00 7c 0a 64 01 6b 28 00 00 72 15 74 03 | ........|...........|.d.k(..r.t. |
| 1f20 | 00 00 00 00 00 00 00 00 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 0d ab 01 | ........j...................d... |
| 1f40 | 00 00 00 00 00 00 82 01 74 0d 00 00 00 00 00 00 00 00 7c 08 ab 01 00 00 00 00 00 00 7c 09 64 03 | ........t.........|.........|.d. |
| 1f60 | 7a 00 00 00 7c 00 7a 05 00 00 6b 37 00 00 72 01 8c db 8c f6 04 00 7c 06 6a 1b 00 00 00 00 00 00 | z...|.z...k7..r.......|.j....... |
| 1f80 | 00 00 00 00 00 00 00 00 00 00 00 00 7c 08 ab 01 00 00 00 00 00 00 01 00 7c 06 53 00 63 02 01 00 | ............|...........|.S.c... |
| 1fa0 | 63 03 7d 0d 7d 0c 77 00 29 0e 61 ab 06 00 00 55 74 69 6c 69 74 79 20 66 6f 72 20 63 72 65 61 74 | c.}.}.w.).a....Utility.for.creat |
| 1fc0 | 69 6e 67 20 61 20 72 61 6e 64 6f 6d 20 72 65 67 75 6c 61 72 20 65 78 70 61 6e 64 65 72 2e 0a 0a | ing.a.random.regular.expander... |
| 1fe0 | 20 20 20 20 52 65 74 75 72 6e 73 20 61 20 72 61 6e 64 6f 6d 20 24 64 24 2d 72 65 67 75 6c 61 72 | ....Returns.a.random.$d$-regular |
| 2000 | 20 67 72 61 70 68 20 6f 6e 20 24 6e 24 20 6e 6f 64 65 73 20 77 68 69 63 68 20 69 73 20 61 6e 20 | .graph.on.$n$.nodes.which.is.an. |
| 2020 | 65 78 70 61 6e 64 65 72 0a 20 20 20 20 67 72 61 70 68 20 77 69 74 68 20 76 65 72 79 20 67 6f 6f | expander.....graph.with.very.goo |
| 2040 | 64 20 70 72 6f 62 61 62 69 6c 69 74 79 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 | d.probability.......Parameters.. |
| 2060 | 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6e 20 3a 20 69 6e 74 0a 20 20 20 20 20 20 | ...----------.....n.:.int....... |
| 2080 | 54 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 6e 6f 64 65 73 2e 0a 20 20 20 20 64 20 3a 20 69 6e 74 | The.number.of.nodes......d.:.int |
| 20a0 | 0a 20 20 20 20 20 20 54 68 65 20 64 65 67 72 65 65 20 6f 66 20 65 61 63 68 20 6e 6f 64 65 2e 0a | .......The.degree.of.each.node.. |
| 20c0 | 20 20 20 20 63 72 65 61 74 65 5f 75 73 69 6e 67 20 3a 20 47 72 61 70 68 20 49 6e 73 74 61 6e 63 | ....create_using.:.Graph.Instanc |
| 20e0 | 65 20 6f 72 20 43 6f 6e 73 74 72 75 63 74 6f 72 0a 20 20 20 20 20 20 49 6e 64 69 63 61 74 6f 72 | e.or.Constructor.......Indicator |
| 2100 | 20 6f 66 20 74 79 70 65 20 6f 66 20 67 72 61 70 68 20 74 6f 20 72 65 74 75 72 6e 2e 0a 20 20 20 | .of.type.of.graph.to.return..... |
| 2120 | 20 20 20 49 66 20 61 20 47 72 61 70 68 2d 74 79 70 65 20 69 6e 73 74 61 6e 63 65 2c 20 74 68 65 | ...If.a.Graph-type.instance,.the |
| 2140 | 6e 20 63 6c 65 61 72 20 61 6e 64 20 75 73 65 20 69 74 2e 0a 20 20 20 20 20 20 49 66 20 61 20 63 | n.clear.and.use.it........If.a.c |
| 2160 | 6f 6e 73 74 72 75 63 74 6f 72 2c 20 63 61 6c 6c 20 69 74 20 74 6f 20 63 72 65 61 74 65 20 61 6e | onstructor,.call.it.to.create.an |
| 2180 | 20 65 6d 70 74 79 20 67 72 61 70 68 2e 0a 20 20 20 20 20 20 55 73 65 20 74 68 65 20 47 72 61 70 | .empty.graph........Use.the.Grap |
| 21a0 | 68 20 63 6f 6e 73 74 72 75 63 74 6f 72 20 62 79 20 64 65 66 61 75 6c 74 2e 0a 20 20 20 20 6d 61 | h.constructor.by.default......ma |
| 21c0 | 78 5f 74 72 69 65 73 20 3a 20 69 6e 74 2e 20 28 64 65 66 61 75 6c 74 3a 20 31 30 30 29 0a 20 20 | x_tries.:.int..(default:.100)... |
| 21e0 | 20 20 20 20 54 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 61 6c 6c 6f 77 65 64 20 6c 6f 6f 70 73 20 | ....The.number.of.allowed.loops. |
| 2200 | 77 68 65 6e 20 67 65 6e 65 72 61 74 69 6e 67 20 65 61 63 68 20 69 6e 64 65 70 65 6e 64 65 6e 74 | when.generating.each.independent |
| 2220 | 20 63 79 63 6c 65 0a 20 20 20 20 73 65 65 64 20 3a 20 28 64 65 66 61 75 6c 74 3a 20 4e 6f 6e 65 | .cycle.....seed.:.(default:.None |
| 2240 | 29 0a 20 20 20 20 20 20 53 65 65 64 20 75 73 65 64 20 74 6f 20 73 65 74 20 72 61 6e 64 6f 6d 20 | ).......Seed.used.to.set.random. |
| 2260 | 6e 75 6d 62 65 72 20 67 65 6e 65 72 61 74 69 6f 6e 20 73 74 61 74 65 2e 20 53 65 65 20 3a 72 65 | number.generation.state..See.:re |
| 2280 | 66 60 52 61 6e 64 6f 6d 6e 65 73 73 3c 72 61 6e 64 6f 6d 6e 65 73 73 3e 60 2e 0a 0a 20 20 20 20 | f`Randomness<randomness>`....... |
| 22a0 | 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 20 20 20 20 54 68 65 20 6e 6f 64 65 73 20 61 72 | Notes.....-----.....The.nodes.ar |
| 22c0 | 65 20 6e 75 6d 62 65 72 65 64 20 66 72 6f 6d 20 24 30 24 20 74 6f 20 24 6e 20 2d 20 31 24 2e 0a | e.numbered.from.$0$.to.$n.-.1$.. |
| 22e0 | 0a 20 20 20 20 54 68 65 20 67 72 61 70 68 20 69 73 20 67 65 6e 65 72 61 74 65 64 20 62 79 20 74 | .....The.graph.is.generated.by.t |
| 2300 | 61 6b 69 6e 67 20 24 64 20 2f 20 32 24 20 72 61 6e 64 6f 6d 20 69 6e 64 65 70 65 6e 64 65 6e 74 | aking.$d./.2$.random.independent |
| 2320 | 20 63 79 63 6c 65 73 2e 0a 0a 20 20 20 20 4a 6f 65 6c 20 46 72 69 65 64 6d 61 6e 20 70 72 6f 76 | .cycles.......Joel.Friedman.prov |
| 2340 | 65 64 20 74 68 61 74 20 69 6e 20 74 68 69 73 20 6d 6f 64 65 6c 20 74 68 65 20 72 65 73 75 6c 74 | ed.that.in.this.model.the.result |
| 2360 | 69 6e 67 0a 20 20 20 20 67 72 61 70 68 20 69 73 20 61 6e 20 65 78 70 61 6e 64 65 72 20 77 69 74 | ing.....graph.is.an.expander.wit |
| 2380 | 68 20 70 72 6f 62 61 62 69 6c 69 74 79 0a 20 20 20 20 24 31 20 2d 20 4f 28 6e 5e 7b 2d 5c 74 61 | h.probability.....$1.-.O(n^{-\ta |
| 23a0 | 75 7d 29 24 20 77 68 65 72 65 20 24 5c 74 61 75 20 3d 20 5c 6c 63 65 69 6c 20 28 5c 73 71 72 74 | u})$.where.$\tau.=.\lceil.(\sqrt |
| 23c0 | 7b 64 20 2d 20 31 7d 29 20 2f 20 32 20 5c 72 63 65 69 6c 20 2d 20 31 24 2e 20 5b 31 5d 5f 0a 0a | {d.-.1})./.2.\rceil.-.1$..[1]_.. |
| 23e0 | 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 20 20 20 20 3e 3e | ....Examples.....--------.....>> |
| 2400 | 3e 20 47 20 3d 20 6e 78 2e 6d 61 79 62 65 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 28 | >.G.=.nx.maybe_regular_expander( |
| 2420 | 6e 3d 32 30 30 2c 20 64 3d 36 2c 20 73 65 65 64 3d 38 30 32 30 29 0a 0a 20 20 20 20 52 65 74 75 | n=200,.d=6,.seed=8020)......Retu |
| 2440 | 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 20 3a 20 67 72 61 70 68 0a 20 20 | rns.....-------.....G.:.graph... |
| 2460 | 20 20 20 20 20 20 54 68 65 20 63 6f 6e 73 74 72 75 63 74 65 64 20 75 6e 64 69 72 65 63 74 65 64 | ......The.constructed.undirected |
| 2480 | 20 67 72 61 70 68 2e 0a 0a 20 20 20 20 52 61 69 73 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 0a 20 | .graph.......Raises.....------.. |
| 24a0 | 20 20 20 4e 65 74 77 6f 72 6b 58 45 72 72 6f 72 0a 20 20 20 20 20 20 20 20 49 66 20 24 64 20 25 | ...NetworkXError.........If.$d.% |
| 24c0 | 20 32 20 21 3d 20 30 24 20 61 73 20 74 68 65 20 64 65 67 72 65 65 20 6d 75 73 74 20 62 65 20 65 | .2.!=.0$.as.the.degree.must.be.e |
| 24e0 | 76 65 6e 2e 0a 20 20 20 20 20 20 20 20 49 66 20 24 6e 20 2d 20 31 24 20 69 73 20 6c 65 73 73 20 | ven..........If.$n.-.1$.is.less. |
| 2500 | 74 68 61 6e 20 24 20 32 64 20 24 20 61 73 20 74 68 65 20 67 72 61 70 68 20 69 73 20 63 6f 6d 70 | than.$.2d.$.as.the.graph.is.comp |
| 2520 | 6c 65 74 65 20 61 74 20 6d 6f 73 74 2e 0a 20 20 20 20 20 20 20 20 49 66 20 6d 61 78 5f 74 72 69 | lete.at.most..........If.max_tri |
| 2540 | 65 73 20 69 73 20 72 65 61 63 68 65 64 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 | es.is.reached......See.Also..... |
| 2560 | 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 69 73 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 | --------.....is_regular_expander |
| 2580 | 0a 20 20 20 20 72 61 6e 64 6f 6d 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 5f 67 72 61 | .....random_regular_expander_gra |
| 25a0 | 70 68 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d | ph......References.....--------- |
| 25c0 | 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 4a 6f 65 6c 20 46 72 69 65 64 6d 61 6e 2c 0a 20 20 20 20 | -........[1].Joel.Friedman,..... |
| 25e0 | 20 20 20 41 20 50 72 6f 6f 66 20 6f 66 20 41 6c 6f 6e 27 73 20 53 65 63 6f 6e 64 20 45 69 67 65 | ...A.Proof.of.Alon's.Second.Eige |
| 2600 | 6e 76 61 6c 75 65 20 43 6f 6e 6a 65 63 74 75 72 65 20 61 6e 64 20 52 65 6c 61 74 65 64 20 50 72 | nvalue.Conjecture.and.Related.Pr |
| 2620 | 6f 62 6c 65 6d 73 2c 20 32 30 30 34 0a 20 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 61 72 78 69 | oblems,.2004........https://arxi |
| 2640 | 76 2e 6f 72 67 2f 61 62 73 2f 63 73 2f 30 34 30 35 30 32 30 0a 0a 20 20 20 20 72 02 00 00 00 4e | v.org/abs/cs/0405020......r....N |
| 2660 | 72 11 00 00 00 7a 1c 6e 20 6d 75 73 74 20 62 65 20 61 20 70 6f 73 69 74 69 76 65 20 69 6e 74 65 | r....z.n.must.be.a.positive.inte |
| 2680 | 67 65 72 72 0f 00 00 00 7a 24 64 20 6d 75 73 74 20 62 65 20 67 72 65 61 74 65 72 20 74 68 61 6e | gerr....z$d.must.be.greater.than |
| 26a0 | 20 6f 72 20 65 71 75 61 6c 20 74 6f 20 32 7a 0e 64 20 6d 75 73 74 20 62 65 20 65 76 65 6e 7a 1e | .or.equal.to.2z.d.must.be.evenz. |
| 26c0 | 4e 65 65 64 20 6e 2d 31 3e 3d 20 64 20 74 6f 20 68 61 76 65 20 72 6f 6f 6d 20 66 6f 72 20 7a 19 | Need.n-1>=.d.to.have.room.for.z. |
| 26e0 | 20 69 6e 64 65 70 65 6e 64 65 6e 74 20 63 79 63 6c 65 73 20 77 69 74 68 20 7a 06 20 6e 6f 64 65 | .independent.cycles.with.z..node |
| 2700 | 73 54 29 01 da 06 63 79 63 6c 69 63 7a 2d 54 6f 6f 20 6d 61 6e 79 20 69 74 65 72 61 74 69 6f 6e | sT)...cyclicz-Too.many.iteration |
| 2720 | 73 20 69 6e 20 6d 61 79 62 65 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 29 0e da 05 6e | s.in.maybe_regular_expander)...n |
| 2740 | 75 6d 70 79 72 14 00 00 00 72 19 00 00 00 72 15 00 00 00 da 03 73 65 74 72 1c 00 00 00 da 03 6c | umpyr....r....r......setr......l |
| 2760 | 65 6e da 0b 70 65 72 6d 75 74 61 74 69 6f 6e da 06 74 6f 6c 69 73 74 da 06 61 70 70 65 6e 64 da | en..permutation..tolist..append. |
| 2780 | 05 75 74 69 6c 73 da 08 70 61 69 72 77 69 73 65 da 06 75 70 64 61 74 65 da 0e 61 64 64 5f 65 64 | .utils..pairwise..update..add_ed |
| 27a0 | 67 65 73 5f 66 72 6f 6d 29 0f 72 1f 00 00 00 da 01 64 72 20 00 00 00 72 36 00 00 00 72 33 00 00 | ges_from).r......dr....r6...r3.. |
| 27c0 | 00 da 02 6e 70 72 21 00 00 00 da 06 63 79 63 6c 65 73 da 05 65 64 67 65 73 da 01 69 da 0a 69 74 | ...npr!.....cycles..edges..i..it |
| 27e0 | 65 72 61 74 69 6f 6e 73 da 05 63 79 63 6c 65 72 25 00 00 00 72 26 00 00 00 da 09 6e 65 77 5f 65 | erations..cycler%...r&.....new_e |
| 2800 | 64 67 65 73 73 0f 00 00 00 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 72 27 00 00 00 72 06 00 | dgess...................r'...r.. |
| 2820 | 00 00 72 06 00 00 00 d9 00 00 00 73 e4 01 00 00 80 00 f3 7e 01 00 05 17 e0 07 08 88 31 82 75 dc | ..r........s.......~........1.u. |
| 2840 | 0e 10 d7 0e 1e d1 0e 1e d0 1f 3d d3 0e 3e d0 08 3e e0 0c 0d 90 11 8a 46 dc 0e 10 d7 0e 1e d1 0e | ..........=..>..>......F........ |
| 2860 | 1e d0 1f 45 d3 0e 46 d0 08 46 e0 0c 0d 90 01 89 45 90 51 8a 4a dc 0e 10 d7 0e 1e d1 0e 1e d0 1f | ...E..F..F......E.Q.J........... |
| 2880 | 2f d3 0e 30 d0 08 30 e0 0c 0d 90 01 89 45 90 51 8a 4a dc 0e 10 d7 0e 1e d1 0e 1e d8 0e 2c a8 51 | /..0..0......E.Q.J...........,.Q |
| 28a0 | b0 21 a9 56 a8 48 d0 34 4d c8 61 c8 53 d0 50 56 d0 0c 57 f3 03 02 0f 0a f0 00 02 09 0a f4 08 00 | .!.V.H.4M.a.S.PV..W............. |
| 28c0 | 09 0b 8f 0e 89 0e 90 71 98 2c d3 08 27 80 41 e0 07 08 88 31 82 75 d8 0f 10 88 08 e0 0d 0f 80 46 | .......q.,..'.A....1.u.........F |
| 28e0 | dc 0c 0f 8b 45 80 45 f4 06 00 0e 13 90 31 98 01 91 36 8b 5d f2 00 16 05 58 01 88 01 d8 15 1e 88 | ....E.E......1...6.]....X....... |
| 2900 | 0a e4 0e 11 90 25 8b 6a 98 51 a0 11 99 55 a0 61 99 4b d3 0e 27 d8 0c 16 98 21 89 4f 88 4a f0 06 | .....%.j.Q...U.a.K..'....!.O.J.. |
| 2920 | 00 15 19 d7 14 24 d1 14 24 a0 51 a8 11 a1 55 d3 14 2b d7 14 32 d1 14 32 d3 14 34 88 45 d8 0c 11 | .....$..$.Q...U..+..2..2..4.E... |
| 2940 | 8f 4c 89 4c 98 11 98 51 99 15 d4 0c 1f f4 08 00 1d 1f 9f 48 99 48 d7 1c 2d d1 1c 2d a8 65 b8 44 | .L.L...Q...........H.H..-..-.e.D |
| 2960 | d0 1c 2d d3 1c 41 f7 05 04 19 0e e1 14 18 90 41 90 71 d8 14 15 90 71 90 36 a0 15 d1 13 26 a8 41 | ..-..A.........A.q....q.6....&.A |
| 2980 | a8 71 a8 36 b8 15 d1 2b 3e f0 05 00 12 13 90 41 92 06 f0 03 04 19 0e 88 49 f1 00 04 19 0e f4 0e | .q.6...+>......A........I....... |
| 29a0 | 00 10 13 90 39 8b 7e a0 11 d2 0f 22 d8 10 16 97 0d 91 0d 98 65 d4 10 24 d8 10 15 97 0c 91 0c 98 | ....9.~...."........e..$........ |
| 29c0 | 59 d4 10 27 e0 0f 19 98 51 8a 7f dc 16 18 d7 16 26 d1 16 26 d0 27 56 d3 16 57 d0 10 57 f4 27 00 | Y..'....Q.......&..&.'V..W..W.'. |
| 29e0 | 0f 12 90 25 8b 6a 98 51 a0 11 99 55 a0 61 99 4b d4 0e 27 f0 07 16 05 58 01 f0 30 00 05 06 d7 04 | ...%.j.Q...U.a.K..'....X..0..... |
| 2a00 | 14 d1 04 14 90 55 d4 04 1b e0 0b 0c 80 48 f9 f3 21 04 19 0e 73 06 00 00 00 c4 2d 1a 46 3e 08 da | .....U.......H..!...s.....-.F>.. |
| 2a20 | 08 64 69 72 65 63 74 65 64 da 0a 6d 75 6c 74 69 67 72 61 70 68 72 21 00 00 00 da 06 77 65 69 67 | .directed..multigraphr!.....weig |
| 2a40 | 68 74 72 11 00 00 00 29 01 da 13 70 72 65 73 65 72 76 65 5f 65 64 67 65 5f 61 74 74 72 73 a9 01 | htr....)...preserve_edge_attrs.. |
| 2a60 | da 07 65 70 73 69 6c 6f 6e 63 01 00 00 00 00 00 00 00 01 00 00 00 08 00 00 00 03 00 00 00 f3 c6 | ..epsilonc...................... |
| 2a80 | 01 00 00 97 00 64 01 64 02 6c 00 7d 02 64 01 64 02 6c 01 7d 03 7c 01 64 01 6b 02 00 00 72 15 74 | .....d.d.l.}.d.d.l.}.|.d.k...r.t |
| 2aa0 | 05 00 00 00 00 00 00 00 00 6a 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 03 ab | .........j...................d.. |
| 2ac0 | 01 00 00 00 00 00 00 82 01 74 05 00 00 00 00 00 00 00 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 | .........t.........j............ |
| 2ae0 | 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 73 01 79 04 74 04 00 00 00 00 00 00 00 00 6a | .......|.........s.y.t.........j |
| 2b00 | 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 0d 00 00 00 00 00 00 00 00 00 00 00 | ...................j............ |
| 2b20 | 00 00 00 00 00 00 00 7c 00 6a 0e 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 01 00 | .......|.j...................... |
| 2b40 | 00 00 00 00 00 5c 02 00 00 7d 04 7d 05 74 05 00 00 00 00 00 00 00 00 6a 10 00 00 00 00 00 00 00 | .....\...}.}.t.........j........ |
| 2b60 | 00 00 00 00 00 00 00 00 00 00 00 7c 00 74 12 00 00 00 00 00 00 00 00 ac 05 ab 02 00 00 00 00 00 | ...........|.t.................. |
| 2b80 | 00 7d 06 7c 03 6a 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 16 00 00 00 00 00 | .}.|.j...................j...... |
| 2ba0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 19 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | .............j.................. |
| 2bc0 | 00 7c 06 64 06 64 07 64 04 ac 08 ab 04 00 00 00 00 00 00 7d 07 74 1b 00 00 00 00 00 00 00 00 7c | .|.d.d.d...........}.t.........| |
| 2be0 | 07 ab 01 00 00 00 00 00 00 7d 08 74 1d 00 00 00 00 00 00 00 00 74 1f 00 00 00 00 00 00 00 00 7c | .........}.t.........t.........| |
| 2c00 | 08 ab 01 00 00 00 00 00 00 64 07 7c 02 6a 21 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | .........d.|.j!................. |
| 2c20 | 00 7c 05 64 09 7a 0a 00 00 ab 01 00 00 00 00 00 00 7a 05 00 00 7c 01 7a 00 00 00 6b 02 00 00 ab | .|.d.z...........z...|.z...k.... |
| 2c40 | 01 00 00 00 00 00 00 53 00 29 0a 61 1f 05 00 00 44 65 74 65 72 6d 69 6e 65 73 20 77 68 65 74 68 | .......S.).a....Determines.wheth |
| 2c60 | 65 72 20 74 68 65 20 67 72 61 70 68 20 47 20 69 73 20 61 20 72 65 67 75 6c 61 72 20 65 78 70 61 | er.the.graph.G.is.a.regular.expa |
| 2c80 | 6e 64 65 72 2e 20 5b 31 5d 5f 0a 0a 20 20 20 20 41 6e 20 65 78 70 61 6e 64 65 72 20 67 72 61 70 | nder..[1]_......An.expander.grap |
| 2ca0 | 68 20 69 73 20 61 20 73 70 61 72 73 65 20 67 72 61 70 68 20 77 69 74 68 20 73 74 72 6f 6e 67 20 | h.is.a.sparse.graph.with.strong. |
| 2cc0 | 63 6f 6e 6e 65 63 74 69 76 69 74 79 20 70 72 6f 70 65 72 74 69 65 73 2e 0a 0a 20 20 20 20 4d 6f | connectivity.properties.......Mo |
| 2ce0 | 72 65 20 70 72 65 63 69 73 65 6c 79 2c 20 74 68 69 73 20 68 65 6c 70 65 72 20 63 68 65 63 6b 73 | re.precisely,.this.helper.checks |
| 2d00 | 20 77 68 65 74 68 65 72 20 74 68 65 20 67 72 61 70 68 20 69 73 20 61 0a 20 20 20 20 72 65 67 75 | .whether.the.graph.is.a.....regu |
| 2d20 | 6c 61 72 20 24 28 6e 2c 20 64 2c 20 5c 6c 61 6d 62 64 61 29 24 2d 65 78 70 61 6e 64 65 72 20 77 | lar.$(n,.d,.\lambda)$-expander.w |
| 2d40 | 69 74 68 20 24 5c 6c 61 6d 62 64 61 24 20 63 6c 6f 73 65 20 74 6f 0a 20 20 20 20 74 68 65 20 41 | ith.$\lambda$.close.to.....the.A |
| 2d60 | 6c 6f 6e 2d 42 6f 70 70 61 6e 61 20 62 6f 75 6e 64 20 61 6e 64 20 67 69 76 65 6e 20 62 79 0a 20 | lon-Boppana.bound.and.given.by.. |
| 2d80 | 20 20 20 24 5c 6c 61 6d 62 64 61 20 3d 20 32 20 5c 73 71 72 74 7b 64 20 2d 20 31 7d 20 2b 20 5c | ...$\lambda.=.2.\sqrt{d.-.1}.+.\ |
| 2da0 | 65 70 73 69 6c 6f 6e 24 2e 20 5b 32 5d 5f 0a 0a 20 20 20 20 49 6e 20 74 68 65 20 63 61 73 65 20 | epsilon$..[2]_......In.the.case. |
| 2dc0 | 77 68 65 72 65 20 24 5c 65 70 73 69 6c 6f 6e 20 3d 20 30 24 20 74 68 65 6e 20 69 66 20 74 68 65 | where.$\epsilon.=.0$.then.if.the |
| 2de0 | 20 67 72 61 70 68 20 73 75 63 63 65 73 73 66 75 6c 6c 79 20 70 61 73 73 65 73 20 74 68 65 20 74 | .graph.successfully.passes.the.t |
| 2e00 | 65 73 74 0a 20 20 20 20 69 74 20 69 73 20 61 20 52 61 6d 61 6e 75 6a 61 6e 20 67 72 61 70 68 2e | est.....it.is.a.Ramanujan.graph. |
| 2e20 | 20 5b 33 5d 5f 0a 0a 20 20 20 20 41 20 52 61 6d 61 6e 75 6a 61 6e 20 67 72 61 70 68 20 68 61 73 | .[3]_......A.Ramanujan.graph.has |
| 2e40 | 20 73 70 65 63 74 72 61 6c 20 67 61 70 20 61 6c 6d 6f 73 74 20 61 73 20 6c 61 72 67 65 20 61 73 | .spectral.gap.almost.as.large.as |
| 2e60 | 20 70 6f 73 73 69 62 6c 65 2c 20 77 68 69 63 68 20 6d 61 6b 65 73 20 74 68 65 6d 0a 20 20 20 20 | .possible,.which.makes.them..... |
| 2e80 | 65 78 63 65 6c 6c 65 6e 74 20 65 78 70 61 6e 64 65 72 73 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 | excellent.expanders.......Parame |
| 2ea0 | 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 20 3a 20 4e 65 74 77 | ters.....----------.....G.:.Netw |
| 2ec0 | 6f 72 6b 58 20 67 72 61 70 68 0a 20 20 20 20 65 70 73 69 6c 6f 6e 20 3a 20 69 6e 74 2c 20 66 6c | orkX.graph.....epsilon.:.int,.fl |
| 2ee0 | 6f 61 74 2c 20 64 65 66 61 75 6c 74 3d 30 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 | oat,.default=0......Returns..... |
| 2f00 | 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 62 6f 6f 6c 0a 20 20 20 20 20 20 20 20 57 68 65 74 68 65 72 | -------.....bool.........Whether |
| 2f20 | 20 74 68 65 20 67 69 76 65 6e 20 67 72 61 70 68 20 69 73 20 61 20 72 65 67 75 6c 61 72 20 24 28 | .the.given.graph.is.a.regular.$( |
| 2f40 | 6e 2c 20 64 2c 20 5c 6c 61 6d 62 64 61 29 24 2d 65 78 70 61 6e 64 65 72 0a 20 20 20 20 20 20 20 | n,.d,.\lambda)$-expander........ |
| 2f60 | 20 77 68 65 72 65 20 24 5c 6c 61 6d 62 64 61 20 3d 20 32 20 5c 73 71 72 74 7b 64 20 2d 20 31 7d | .where.$\lambda.=.2.\sqrt{d.-.1} |
| 2f80 | 20 2b 20 5c 65 70 73 69 6c 6f 6e 24 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 | .+.\epsilon$.......Examples..... |
| 2fa0 | 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 72 61 6e 64 6f 6d 5f 72 | --------.....>>>.G.=.nx.random_r |
| 2fc0 | 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 5f 67 72 61 70 68 28 32 30 2c 20 34 29 0a 20 20 20 | egular_expander_graph(20,.4).... |
| 2fe0 | 20 3e 3e 3e 20 6e 78 2e 69 73 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 28 47 29 0a 20 | .>>>.nx.is_regular_expander(G).. |
| 3000 | 20 20 20 54 72 75 65 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d 2d 2d 2d 2d | ...True......See.Also.....------ |
| 3020 | 2d 2d 0a 20 20 20 20 6d 61 79 62 65 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 0a 20 20 | --.....maybe_regular_expander... |
| 3040 | 20 20 72 61 6e 64 6f 6d 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 5f 67 72 61 70 68 0a | ..random_regular_expander_graph. |
| 3060 | 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 | .....References.....----------.. |
| 3080 | 20 20 20 2e 2e 20 5b 31 5d 20 45 78 70 61 6e 64 65 72 20 67 72 61 70 68 2c 20 68 74 74 70 73 3a | ......[1].Expander.graph,.https: |
| 30a0 | 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 45 78 70 61 6e 64 65 72 | //en.wikipedia.org/wiki/Expander |
| 30c0 | 5f 67 72 61 70 68 0a 20 20 20 20 2e 2e 20 5b 32 5d 20 41 6c 6f 6e 2d 42 6f 70 70 61 6e 61 20 62 | _graph........[2].Alon-Boppana.b |
| 30e0 | 6f 75 6e 64 2c 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 | ound,.https://en.wikipedia.org/w |
| 3100 | 69 6b 69 2f 41 6c 6f 6e 25 45 32 25 38 30 25 39 33 42 6f 70 70 61 6e 61 5f 62 6f 75 6e 64 0a 20 | iki/Alon%E2%80%93Boppana_bound.. |
| 3120 | 20 20 20 2e 2e 20 5b 33 5d 20 52 61 6d 61 6e 75 6a 61 6e 20 67 72 61 70 68 73 2c 20 68 74 74 70 | ......[3].Ramanujan.graphs,.http |
| 3140 | 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 52 61 6d 61 6e 75 | s://en.wikipedia.org/wiki/Ramanu |
| 3160 | 6a 61 6e 5f 67 72 61 70 68 0a 0a 20 20 20 20 72 02 00 00 00 4e 7a 1c 65 70 73 69 6c 6f 6e 20 6d | jan_graph......r....Nz.epsilon.m |
| 3180 | 75 73 74 20 62 65 20 6e 6f 6e 20 6e 65 67 61 74 69 76 65 46 29 01 da 05 64 74 79 70 65 da 02 4c | ust.be.non.negativeF)...dtype..L |
| 31a0 | 4d 72 0f 00 00 00 29 03 da 05 77 68 69 63 68 da 01 6b da 13 72 65 74 75 72 6e 5f 65 69 67 65 6e | Mr....)...which..k..return_eigen |
| 31c0 | 76 65 63 74 6f 72 73 72 11 00 00 00 29 11 72 39 00 00 00 da 05 73 63 69 70 79 72 14 00 00 00 72 | vectorsr....).r9.....scipyr....r |
| 31e0 | 19 00 00 00 da 0a 69 73 5f 72 65 67 75 6c 61 72 72 3f 00 00 00 da 11 61 72 62 69 74 72 61 72 79 | ......is_regularr?.....arbitrary |
| 3200 | 5f 65 6c 65 6d 65 6e 74 da 06 64 65 67 72 65 65 da 10 61 64 6a 61 63 65 6e 63 79 5f 6d 61 74 72 | _element..degree..adjacency_matr |
| 3220 | 69 78 da 05 66 6c 6f 61 74 da 06 73 70 61 72 73 65 da 06 6c 69 6e 61 6c 67 da 05 65 69 67 73 68 | ix..float..sparse..linalg..eigsh |
| 3240 | da 03 6d 69 6e da 04 62 6f 6f 6c da 03 61 62 73 da 04 73 71 72 74 29 09 72 21 00 00 00 72 50 00 | ..min..bool..abs..sqrt).r!...rP. |
| 3260 | 00 00 72 44 00 00 00 da 02 73 70 da 01 5f 72 43 00 00 00 da 01 41 da 04 6c 61 6d 73 da 07 6c 61 | ..rD.....sp.._rC.....A..lams..la |
| 3280 | 6d 62 64 61 32 73 09 00 00 00 20 20 20 20 20 20 20 20 20 72 27 00 00 00 72 07 00 00 00 72 07 00 | mbda2s.............r'...r....r.. |
| 32a0 | 00 00 4e 01 00 00 73 bb 00 00 00 80 00 f3 62 01 00 05 17 db 04 16 e0 07 0e 90 11 82 7b dc 0e 10 | ..N...s.......b.............{... |
| 32c0 | d7 0e 1e d1 0e 1e d0 1f 3d d3 0e 3e d0 08 3e e4 0b 0d 8f 3d 89 3d 98 11 d4 0b 1b d8 0f 14 e4 0b | ........=..>..>....=.=.......... |
| 32e0 | 0d 8f 38 89 38 d7 0b 25 d1 0b 25 a0 61 a7 68 a1 68 d3 0b 2f 81 44 80 41 80 71 e4 08 0a d7 08 1b | ..8.8..%..%.a.h.h../.D.A.q...... |
| 3300 | d1 08 1b 98 41 a4 55 d4 08 2b 80 41 d8 0b 0d 8f 39 89 39 d7 0b 1b d1 0b 1b d7 0b 21 d1 0b 21 a0 | ....A.U..+.A....9.9........!..!. |
| 3320 | 21 a8 34 b0 31 c8 25 d0 0b 21 d3 0b 50 80 44 f4 06 00 0f 12 90 24 8b 69 80 47 f4 06 00 0c 10 94 | !.4.1.%..!..P.D......$.i.G...... |
| 3340 | 03 90 47 93 0c 98 71 a0 32 a7 37 a1 37 a8 31 a8 71 a9 35 a3 3e d1 1f 31 b0 47 d1 1f 3b d1 10 3b | ..G...q.2.7.7.1.q.5.>..1.G..;..; |
| 3360 | d3 0b 3c d0 04 3c 72 28 00 00 00 29 04 72 50 00 00 00 72 20 00 00 00 72 36 00 00 00 72 33 00 00 | ..<..<r(...).rP...r....r6...r3.. |
| 3380 | 00 63 02 00 00 00 00 00 00 00 04 00 00 00 07 00 00 00 03 00 00 00 f3 be 00 00 00 97 00 74 01 00 | .c...........................t.. |
| 33a0 | 00 00 00 00 00 00 00 7c 00 7c 01 7c 03 7c 04 7c 05 ac 01 ab 05 00 00 00 00 00 00 7d 06 7c 04 7d | .......|.|.|.|.|...........}.|.} |
| 33c0 | 07 74 03 00 00 00 00 00 00 00 00 7c 06 7c 02 ac 02 ab 02 00 00 00 00 00 00 73 3d 7c 07 64 03 7a | .t.........|.|...........s=|.d.z |
| 33e0 | 17 00 00 7d 07 74 01 00 00 00 00 00 00 00 00 7c 00 7c 01 7c 03 7c 04 7c 05 ac 04 ab 05 00 00 00 | ...}.t.........|.|.|.|.|........ |
| 3400 | 00 00 00 7d 06 7c 07 64 05 6b 28 00 00 72 15 74 05 00 00 00 00 00 00 00 00 6a 06 00 00 00 00 00 | ...}.|.d.k(..r.t.........j...... |
| 3420 | 00 00 00 00 00 00 00 00 00 00 00 00 00 64 06 ab 01 00 00 00 00 00 00 82 01 74 03 00 00 00 00 00 | .............d...........t...... |
| 3440 | 00 00 00 7c 06 7c 02 ac 02 ab 02 00 00 00 00 00 00 73 01 8c 3d 7c 06 53 00 29 07 61 10 06 00 00 | ...|.|...........s..=|.S.).a.... |
| 3460 | 52 65 74 75 72 6e 73 20 61 20 72 61 6e 64 6f 6d 20 72 65 67 75 6c 61 72 20 65 78 70 61 6e 64 65 | Returns.a.random.regular.expande |
| 3480 | 72 20 67 72 61 70 68 20 6f 6e 20 24 6e 24 20 6e 6f 64 65 73 20 77 69 74 68 20 64 65 67 72 65 65 | r.graph.on.$n$.nodes.with.degree |
| 34a0 | 20 24 64 24 2e 0a 0a 20 20 20 20 41 6e 20 65 78 70 61 6e 64 65 72 20 67 72 61 70 68 20 69 73 20 | .$d$.......An.expander.graph.is. |
| 34c0 | 61 20 73 70 61 72 73 65 20 67 72 61 70 68 20 77 69 74 68 20 73 74 72 6f 6e 67 20 63 6f 6e 6e 65 | a.sparse.graph.with.strong.conne |
| 34e0 | 63 74 69 76 69 74 79 20 70 72 6f 70 65 72 74 69 65 73 2e 20 5b 31 5d 5f 0a 0a 20 20 20 20 4d 6f | ctivity.properties..[1]_......Mo |
| 3500 | 72 65 20 70 72 65 63 69 73 65 6c 79 20 74 68 65 20 72 65 74 75 72 6e 65 64 20 67 72 61 70 68 20 | re.precisely.the.returned.graph. |
| 3520 | 69 73 20 61 20 24 28 6e 2c 20 64 2c 20 5c 6c 61 6d 62 64 61 29 24 2d 65 78 70 61 6e 64 65 72 20 | is.a.$(n,.d,.\lambda)$-expander. |
| 3540 | 77 69 74 68 0a 20 20 20 20 24 5c 6c 61 6d 62 64 61 20 3d 20 32 20 5c 73 71 72 74 7b 64 20 2d 20 | with.....$\lambda.=.2.\sqrt{d.-. |
| 3560 | 31 7d 20 2b 20 5c 65 70 73 69 6c 6f 6e 24 2c 20 63 6c 6f 73 65 20 74 6f 20 74 68 65 20 41 6c 6f | 1}.+.\epsilon$,.close.to.the.Alo |
| 3580 | 6e 2d 42 6f 70 70 61 6e 61 20 62 6f 75 6e 64 2e 20 5b 32 5d 5f 0a 0a 20 20 20 20 49 6e 20 74 68 | n-Boppana.bound..[2]_......In.th |
| 35a0 | 65 20 63 61 73 65 20 77 68 65 72 65 20 24 5c 65 70 73 69 6c 6f 6e 20 3d 20 30 24 20 69 74 20 72 | e.case.where.$\epsilon.=.0$.it.r |
| 35c0 | 65 74 75 72 6e 73 20 61 20 52 61 6d 61 6e 75 6a 61 6e 20 67 72 61 70 68 2e 0a 20 20 20 20 41 20 | eturns.a.Ramanujan.graph......A. |
| 35e0 | 52 61 6d 61 6e 75 6a 61 6e 20 67 72 61 70 68 20 68 61 73 20 73 70 65 63 74 72 61 6c 20 67 61 70 | Ramanujan.graph.has.spectral.gap |
| 3600 | 20 61 6c 6d 6f 73 74 20 61 73 20 6c 61 72 67 65 20 61 73 20 70 6f 73 73 69 62 6c 65 2c 0a 20 20 | .almost.as.large.as.possible,... |
| 3620 | 20 20 77 68 69 63 68 20 6d 61 6b 65 73 20 74 68 65 6d 20 65 78 63 65 6c 6c 65 6e 74 20 65 78 70 | ..which.makes.them.excellent.exp |
| 3640 | 61 6e 64 65 72 73 2e 20 5b 33 5d 5f 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 | anders..[3]_......Parameters.... |
| 3660 | 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6e 20 3a 20 69 6e 74 0a 20 20 20 20 20 20 54 68 | .----------.....n.:.int.......Th |
| 3680 | 65 20 6e 75 6d 62 65 72 20 6f 66 20 6e 6f 64 65 73 2e 0a 20 20 20 20 64 20 3a 20 69 6e 74 0a 20 | e.number.of.nodes......d.:.int.. |
| 36a0 | 20 20 20 20 20 54 68 65 20 64 65 67 72 65 65 20 6f 66 20 65 61 63 68 20 6e 6f 64 65 2e 0a 20 20 | .....The.degree.of.each.node.... |
| 36c0 | 20 20 65 70 73 69 6c 6f 6e 20 3a 20 69 6e 74 2c 20 66 6c 6f 61 74 2c 20 64 65 66 61 75 6c 74 3d | ..epsilon.:.int,.float,.default= |
| 36e0 | 30 0a 20 20 20 20 6d 61 78 5f 74 72 69 65 73 20 3a 20 69 6e 74 2c 20 28 64 65 66 61 75 6c 74 3a | 0.....max_tries.:.int,.(default: |
| 3700 | 20 31 30 30 29 0a 20 20 20 20 20 20 54 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 61 6c 6c 6f 77 65 | .100).......The.number.of.allowe |
| 3720 | 64 20 6c 6f 6f 70 73 2c 20 61 6c 73 6f 20 75 73 65 64 20 69 6e 20 74 68 65 20 6d 61 79 62 65 5f | d.loops,.also.used.in.the.maybe_ |
| 3740 | 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 20 75 74 69 6c 69 74 79 0a 20 20 20 20 73 65 65 | regular_expander.utility.....see |
| 3760 | 64 20 3a 20 28 64 65 66 61 75 6c 74 3a 20 4e 6f 6e 65 29 0a 20 20 20 20 20 20 53 65 65 64 20 75 | d.:.(default:.None).......Seed.u |
| 3780 | 73 65 64 20 74 6f 20 73 65 74 20 72 61 6e 64 6f 6d 20 6e 75 6d 62 65 72 20 67 65 6e 65 72 61 74 | sed.to.set.random.number.generat |
| 37a0 | 69 6f 6e 20 73 74 61 74 65 2e 20 53 65 65 20 3a 72 65 66 60 52 61 6e 64 6f 6d 6e 65 73 73 3c 72 | ion.state..See.:ref`Randomness<r |
| 37c0 | 61 6e 64 6f 6d 6e 65 73 73 3e 60 2e 0a 0a 20 20 20 20 52 61 69 73 65 73 0a 20 20 20 20 2d 2d 2d | andomness>`.......Raises.....--- |
| 37e0 | 2d 2d 2d 0a 20 20 20 20 4e 65 74 77 6f 72 6b 58 45 72 72 6f 72 0a 20 20 20 20 20 20 20 20 49 66 | ---.....NetworkXError.........If |
| 3800 | 20 6d 61 78 5f 74 72 69 65 73 20 69 73 20 72 65 61 63 68 65 64 0a 0a 20 20 20 20 45 78 61 6d 70 | .max_tries.is.reached......Examp |
| 3820 | 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. |
| 3840 | 72 61 6e 64 6f 6d 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 5f 67 72 61 70 68 28 32 30 | random_regular_expander_graph(20 |
| 3860 | 2c 20 34 29 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 69 73 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e | ,.4).....>>>.nx.is_regular_expan |
| 3880 | 64 65 72 28 47 29 0a 20 20 20 20 54 72 75 65 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d | der(G).....True......Notes.....- |
| 38a0 | 2d 2d 2d 2d 0a 20 20 20 20 54 68 69 73 20 6c 6f 6f 70 73 20 6f 76 65 72 20 60 6d 61 79 62 65 5f | ----.....This.loops.over.`maybe_ |
| 38c0 | 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 60 20 61 6e 64 20 63 61 6e 20 62 65 20 73 6c 6f | regular_expander`.and.can.be.slo |
| 38e0 | 77 20 77 68 65 6e 0a 20 20 20 20 24 6e 24 20 69 73 20 74 6f 6f 20 62 69 67 20 6f 72 20 24 5c 65 | w.when.....$n$.is.too.big.or.$\e |
| 3900 | 70 73 69 6c 6f 6e 24 20 74 6f 6f 20 73 6d 61 6c 6c 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f | psilon$.too.small.......See.Also |
| 3920 | 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 6d 61 79 62 65 5f 72 65 67 75 6c 61 72 5f | .....--------.....maybe_regular_ |
| 3940 | 65 78 70 61 6e 64 65 72 0a 20 20 20 20 69 73 5f 72 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 | expander.....is_regular_expander |
| 3960 | 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a | ......References.....----------. |
| 3980 | 20 20 20 20 2e 2e 20 5b 31 5d 20 45 78 70 61 6e 64 65 72 20 67 72 61 70 68 2c 20 68 74 74 70 73 | .......[1].Expander.graph,.https |
| 39a0 | 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 45 78 70 61 6e 64 65 | ://en.wikipedia.org/wiki/Expande |
| 39c0 | 72 5f 67 72 61 70 68 0a 20 20 20 20 2e 2e 20 5b 32 5d 20 41 6c 6f 6e 2d 42 6f 70 70 61 6e 61 20 | r_graph........[2].Alon-Boppana. |
| 39e0 | 62 6f 75 6e 64 2c 20 68 74 74 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f | bound,.https://en.wikipedia.org/ |
| 3a00 | 77 69 6b 69 2f 41 6c 6f 6e 25 45 32 25 38 30 25 39 33 42 6f 70 70 61 6e 61 5f 62 6f 75 6e 64 0a | wiki/Alon%E2%80%93Boppana_bound. |
| 3a20 | 20 20 20 20 2e 2e 20 5b 33 5d 20 52 61 6d 61 6e 75 6a 61 6e 20 67 72 61 70 68 73 2c 20 68 74 74 | .......[3].Ramanujan.graphs,.htt |
| 3a40 | 70 73 3a 2f 2f 65 6e 2e 77 69 6b 69 70 65 64 69 61 2e 6f 72 67 2f 77 69 6b 69 2f 52 61 6d 61 6e | ps://en.wikipedia.org/wiki/Raman |
| 3a60 | 75 6a 61 6e 5f 67 72 61 70 68 0a 0a 20 20 20 20 72 35 00 00 00 72 4f 00 00 00 72 11 00 00 00 29 | ujan_graph......r5...rO...r....) |
| 3a80 | 05 72 1f 00 00 00 72 43 00 00 00 72 20 00 00 00 72 36 00 00 00 72 33 00 00 00 72 02 00 00 00 7a | .r....rC...r....r6...r3...r....z |
| 3aa0 | 34 54 6f 6f 20 6d 61 6e 79 20 69 74 65 72 61 74 69 6f 6e 73 20 69 6e 20 72 61 6e 64 6f 6d 5f 72 | 4Too.many.iterations.in.random_r |
| 3ac0 | 65 67 75 6c 61 72 5f 65 78 70 61 6e 64 65 72 5f 67 72 61 70 68 29 04 72 06 00 00 00 72 07 00 00 | egular_expander_graph).r....r... |
| 3ae0 | 00 72 14 00 00 00 72 19 00 00 00 29 08 72 1f 00 00 00 72 43 00 00 00 72 50 00 00 00 72 20 00 00 | .r....r....).r....rC...rP...r... |
| 3b00 | 00 72 36 00 00 00 72 33 00 00 00 72 21 00 00 00 72 48 00 00 00 73 08 00 00 00 20 20 20 20 20 20 | .r6...r3...r!...rH...s.......... |
| 3b20 | 20 20 72 27 00 00 00 72 08 00 00 00 72 08 00 00 00 94 01 00 00 73 7b 00 00 00 80 00 f4 70 01 00 | ..r'...r....r........s{......p.. |
| 3b40 | 09 1f d8 08 09 88 31 98 3c b0 39 c0 34 f4 03 02 09 06 80 41 f0 06 00 12 1b 80 4a e4 0e 21 a0 21 | ......1.<.9.4......A......J..!.! |
| 3b60 | a8 57 d5 0e 35 d8 08 12 90 61 89 0f 88 0a dc 0c 22 d8 0e 0f 90 31 a0 3c b8 39 c8 34 f4 03 02 0d | .W..5....a......"....1.<.9.4.... |
| 3b80 | 0a 88 01 f0 08 00 0c 16 98 11 8a 3f dc 12 14 d7 12 22 d1 12 22 d8 10 46 f3 03 02 13 0e f0 00 02 | ...........?.....".."..F........ |
| 3ba0 | 0d 0e f4 0f 00 0f 22 a0 21 a8 57 d6 0e 35 f0 16 00 0c 0d 80 48 72 28 00 00 00 29 01 4e 29 10 da | ......".!.W..5......Hr(...).N).. |
| 3bc0 | 07 5f 5f 64 6f 63 5f 5f 72 1a 00 00 00 da 08 6e 65 74 77 6f 72 6b 78 72 14 00 00 00 da 07 5f 5f | .__doc__r......networkxr......__ |
| 3be0 | 61 6c 6c 5f 5f da 0d 5f 64 69 73 70 61 74 63 68 61 62 6c 65 72 03 00 00 00 72 04 00 00 00 72 05 | all__.._dispatchabler....r....r. |
| 3c00 | 00 00 00 72 3f 00 00 00 da 0a 64 65 63 6f 72 61 74 6f 72 73 da 0f 6e 70 5f 72 61 6e 64 6f 6d 5f | ...r?.....decorators..np_random_ |
| 3c20 | 73 74 61 74 65 72 06 00 00 00 da 13 6e 6f 74 5f 69 6d 70 6c 65 6d 65 6e 74 65 64 5f 66 6f 72 72 | stater......not_implemented_forr |
| 3c40 | 07 00 00 00 72 08 00 00 00 a9 00 72 28 00 00 00 72 27 00 00 00 fa 08 3c 6d 6f 64 75 6c 65 3e 72 | ....r......r(...r'.....<module>r |
| 3c60 | 72 00 00 00 01 00 00 00 73 75 01 00 00 f0 03 01 01 01 d9 00 39 e3 00 10 e3 00 15 f2 04 07 0b 02 | r.......su..........9........... |
| 3c80 | 80 07 f0 54 01 00 02 12 80 12 d7 01 11 d1 01 11 98 14 a8 54 d4 01 32 f2 02 27 01 0d f3 03 00 02 | ...T...............T..2..'...... |
| 3ca0 | 33 f0 02 27 01 0d f0 54 01 00 02 12 80 12 d7 01 11 d1 01 11 98 14 a8 54 d4 01 32 f2 02 3c 01 0d | 3..'...T...............T..2..<.. |
| 3cc0 | f3 03 00 02 33 f0 02 3c 01 0d f0 7e 01 00 02 12 80 12 d7 01 11 d1 01 11 98 14 a8 54 d4 01 32 f2 | ....3..<...~...............T..2. |
| 3ce0 | 02 39 01 0d f3 03 00 02 33 f0 02 39 01 0d f0 78 01 00 02 04 87 18 81 18 d7 01 14 d1 01 14 d7 01 | .9......3..9...x................ |
| 3d00 | 24 d1 01 24 a0 56 d3 01 2c d8 01 11 80 12 d7 01 11 d1 01 11 98 14 a8 54 d4 01 32 d8 31 35 c0 13 | $..$.V..,..............T..2.15.. |
| 3d20 | c8 34 f3 00 70 01 01 0d f3 03 00 02 33 f3 03 00 02 2d f0 04 70 01 01 0d f0 66 03 00 02 04 87 18 | .4..p.......3....-..p....f...... |
| 3d40 | 81 18 d7 01 1d d1 01 1d 98 6a d3 01 29 d8 01 03 87 18 81 18 d7 01 1d d1 01 1d 98 6c d3 01 2b d8 | .........j..)..............l..+. |
| 3d60 | 01 11 80 12 d7 01 11 d1 01 11 a0 73 a8 58 b0 71 a8 4d d0 26 3a d4 01 3b d8 26 27 f3 00 40 01 01 | ...........s.X.q.M.&:..;.&'..@.. |
| 3d80 | 3d f3 03 00 02 3c f3 03 00 02 2c f3 03 00 02 2a f0 06 40 01 01 3d f0 46 02 00 02 04 87 18 81 18 | =....<....,....*..@..=.F........ |
| 3da0 | d7 01 14 d1 01 14 d7 01 24 d1 01 24 a0 56 d3 01 2c d8 01 11 80 12 d7 01 11 d1 01 11 98 14 a8 54 | ........$..$.V..,..............T |
| 3dc0 | d4 01 32 e0 15 16 a0 54 b0 53 b8 74 f3 03 46 01 01 0d f3 03 00 02 33 f3 03 00 02 2d f1 04 46 01 | ..2....T.S.t..F.......3....-..F. |
| 3de0 | 01 0d 72 28 00 00 00 | ..r(... |
 |
index : uiuc-course-graph.git | |
| Unnamed repository; edit this file 'description' to name the repository. | Ubuntu |
| summaryrefslogtreecommitdiff |
path: root/.venv/lib/python3.12/site-packages/networkx/generators/__pycache__/expanders.cpython-312.pyc
blob: 0cb93cc5841c043bd4cd7b46284b802ba80d6451 (plain)