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0120 63 6f 6d 70 75 74 69 6e 67 20 61 6e 64 20 76 65 72 69 66 79 69 6e 67 20 72 65 67 75 6c 61 72 20 computing.and.verifying.regular.
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0440 65 61 63 68 0a 20 20 20 20 76 65 72 74 65 78 20 61 72 65 20 65 71 75 61 6c 2e 0a 0a 20 20 20 20 each.....vertex.are.equal.......
0460 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 20 Parameters.....----------.....G.
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04a0 20 20 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 ..-------.....bool.........Wheth
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04e0 20 72 65 67 75 6c 61 72 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d 2d 2d .regular.......Examples.....----
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09e0 00 00 00 00 00 00 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 53 00 ............D.................S.
0a00 29 02 61 82 01 00 00 44 65 74 65 72 6d 69 6e 65 73 20 77 68 65 74 68 65 72 20 74 68 65 20 67 72 ).a....Determines.whether.the.gr
0a20 61 70 68 20 60 60 47 60 60 20 69 73 20 61 20 6b 2d 72 65 67 75 6c 61 72 20 67 72 61 70 68 2e 0a aph.``G``.is.a.k-regular.graph..
0a40 0a 20 20 20 20 41 20 6b 2d 72 65 67 75 6c 61 72 20 67 72 61 70 68 20 69 73 20 61 20 67 72 61 70 .....A.k-regular.graph.is.a.grap
0a60 68 20 77 68 65 72 65 20 65 61 63 68 20 76 65 72 74 65 78 20 68 61 73 20 64 65 67 72 65 65 20 6b h.where.each.vertex.has.degree.k
0a80 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.....----------
0aa0 0a 20 20 20 20 47 20 3a 20 4e 65 74 77 6f 72 6b 58 20 67 72 61 70 68 0a 0a 20 20 20 20 52 65 74 .....G.:.NetworkX.graph......Ret
0ac0 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 62 6f 6f 6c 0a 20 20 20 20 20 20 urns.....-------.....bool.......
0ae0 20 20 57 68 65 74 68 65 72 20 74 68 65 20 67 69 76 65 6e 20 67 72 61 70 68 20 69 73 20 6b 2d 72 ..Whether.the.given.graph.is.k-r
0b00 65 67 75 6c 61 72 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 egular.......Examples.....------
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0b40 20 28 32 2c 20 33 29 2c 20 28 33 2c 20 34 29 2c 20 28 34 2c 20 31 29 5d 29 0a 20 20 20 20 3e 3e .(2,.3),.(3,.4),.(4,.1)]).....>>
0b60 3e 20 6e 78 2e 69 73 5f 6b 5f 72 65 67 75 6c 61 72 28 47 2c 20 6b 3d 33 29 0a 20 20 20 20 46 61 >.nx.is_k_regular(G,.k=3).....Fa
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0ba0 00 00 00 95 01 4b 00 01 00 97 00 7c 00 5d 0c 00 00 5c 02 00 00 7d 01 7d 02 7c 02 89 03 6b 28 00 .....K.....|.]...\...}.}.|...k(.
0bc0 00 96 01 97 01 01 00 8c 0e 04 00 79 00 ad 03 77 01 72 09 00 00 00 72 0a 00 00 00 29 04 72 0b 00 ...........y...w.r....r....).r..
0be0 00 00 da 01 6e 72 0d 00 00 00 da 01 6b 73 04 00 00 00 20 20 20 80 72 0f 00 00 00 72 10 00 00 00 ....nr......ks........r....r....
0c00 7a 1f 69 73 5f 6b 5f 72 65 67 75 6c 61 72 2e 3c 6c 6f 63 61 6c 73 3e 2e 3c 67 65 6e 65 78 70 72 z.is_k_regular.<locals>.<genexpr
0c20 3e 46 00 00 00 73 19 00 00 00 f8 e8 00 f8 80 00 d2 0e 2b 99 24 98 21 98 51 88 71 90 41 8d 76 d1 >F...s............+.$.!.Q.q.A.v.
0c40 0e 2b f9 72 11 00 00 00 29 02 72 1d 00 00 00 72 1c 00 00 00 29 02 72 20 00 00 00 72 29 00 00 00 .+.r....).r....r....).r....r)...
0c60 73 02 00 00 00 20 60 72 0f 00 00 00 72 05 00 00 00 72 05 00 00 00 2f 00 00 00 73 1a 00 00 00 f8 s.....`r....r....r..../...s.....
0c80 80 00 f4 2e 00 0c 0f d3 0e 2b a0 21 a7 28 a1 28 d4 0e 2b d3 0b 2b d0 04 2b 72 24 00 00 00 da 0a .........+.!.(.(..+..+..+r$.....
0ca0 6d 75 6c 74 69 67 72 61 70 68 54 29 02 da 13 70 72 65 73 65 72 76 65 5f 65 64 67 65 5f 61 74 74 multigraphT)...preserve_edge_att
0cc0 72 73 da 0d 72 65 74 75 72 6e 73 5f 67 72 61 70 68 63 03 00 00 00 00 00 00 00 00 00 00 00 07 00 rs..returns_graphc..............
0ce0 00 00 03 00 00 00 f3 88 02 00 00 87 01 87 0d 97 00 64 01 64 02 6c 00 6d 01 7d 03 6d 02 7d 04 01 .................d.d.l.m.}.m.}..
0d00 00 02 00 47 00 88 0d 66 01 64 03 84 08 64 04 ab 02 00 00 00 00 00 00 7d 05 02 00 47 00 64 05 84 ...G...f.d...d.........}...G.d..
0d20 00 64 06 ab 02 00 00 00 00 00 00 7d 06 74 07 00 00 00 00 00 00 00 00 88 01 66 01 64 07 84 08 7c .d.........}.t...........f.d...|
0d40 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 44 00 ab 00 00 00 00 00 00 00 ab .j...................D..........
0d60 01 00 00 00 00 00 00 72 15 74 0b 00 00 00 00 00 00 00 00 6a 0c 00 00 00 00 00 00 00 00 00 00 00 .......r.t.........j............
0d80 00 00 00 00 00 00 00 64 08 ab 01 00 00 00 00 00 00 82 01 7c 00 6a 0f 00 00 00 00 00 00 00 00 00 .......d...........|.j..........
0da0 00 00 00 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 8a 0d 67 00 7d 07 74 11 00 00 00 00 00 00 00 ...................g.}.t........
0dc0 00 89 0d 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 44 ...j...........................D
0de0 00 5d 45 00 00 5c 02 00 00 7d 08 7d 09 89 01 7c 09 64 09 7a 0b 00 00 6b 02 00 00 72 0c 02 00 7c .]E..\...}.}...|.d.z...k...r...|
0e00 06 89 01 7c 09 7c 08 89 0d ab 04 00 00 00 00 00 00 7d 0a 6e 0b 02 00 7c 05 89 01 7c 09 7c 08 89 ...|.|...........}.n...|...|.|..
0e20 0d ab 04 00 00 00 00 00 00 7d 0a 7c 0a 6a 13 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .........}.|.j..................
0e40 00 ab 00 00 00 00 00 00 00 01 00 7c 07 6a 15 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ...........|.j..................
0e60 00 7c 0a ab 01 00 00 00 00 00 00 01 00 8c 47 04 00 02 00 7c 04 89 0d 64 0a 7c 02 ac 0b ab 03 00 .|............G....|...d.|......
0e80 00 00 00 00 00 7d 0b 02 00 7c 03 89 0d 7c 0b ab 02 00 00 00 00 00 00 73 15 74 0b 00 00 00 00 00 .....}...|...|.........s.t......
0ea0 00 00 00 6a 0c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 0c ab 01 00 00 00 00 00 ...j...................d........
0ec0 00 82 01 89 0d 6a 17 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 .....j..........................
0ee0 00 44 00 5d 2c 00 00 7d 0c 7c 0c 7c 0b 76 01 73 01 8c 08 7c 0c 64 0d 19 00 00 00 7c 0c 64 01 19 .D.],..}.|.|.v.s...|.d.....|.d..
0f00 00 00 00 66 02 7c 0b 76 01 73 01 8c 15 89 0d 6a 19 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ...f.|.v.s.....j................
0f20 00 00 00 7c 0c 64 01 19 00 00 00 7c 0c 64 0d 19 00 00 00 ab 02 00 00 00 00 00 00 01 00 8c 2e 04 ...|.d.....|.d..................
0f40 00 7c 07 44 00 5d 12 00 00 7d 0a 7c 0a 6a 1b 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .|.D.]...}.|.j..................
0f60 00 ab 00 00 00 00 00 00 00 01 00 8c 14 04 00 89 0d 53 00 29 0e 75 d5 03 00 00 43 6f 6d 70 75 74 .................S.).u....Comput
0f80 65 20 61 20 6b 2d 66 61 63 74 6f 72 20 6f 66 20 47 0a 0a 20 20 20 20 41 20 6b 2d 66 61 63 74 6f e.a.k-factor.of.G......A.k-facto
0fa0 72 20 6f 66 20 61 20 67 72 61 70 68 20 69 73 20 61 20 73 70 61 6e 6e 69 6e 67 20 6b 2d 72 65 67 r.of.a.graph.is.a.spanning.k-reg
0fc0 75 6c 61 72 20 73 75 62 67 72 61 70 68 2e 0a 20 20 20 20 41 20 73 70 61 6e 6e 69 6e 67 20 6b 2d ular.subgraph......A.spanning.k-
0fe0 72 65 67 75 6c 61 72 20 73 75 62 67 72 61 70 68 20 6f 66 20 47 20 69 73 20 61 20 73 75 62 67 72 regular.subgraph.of.G.is.a.subgr
1000 61 70 68 20 74 68 61 74 20 63 6f 6e 74 61 69 6e 73 0a 20 20 20 20 65 61 63 68 20 76 65 72 74 65 aph.that.contains.....each.verte
1020 78 20 6f 66 20 47 20 61 6e 64 20 61 20 73 75 62 73 65 74 20 6f 66 20 74 68 65 20 65 64 67 65 73 x.of.G.and.a.subset.of.the.edges
1040 20 6f 66 20 47 20 73 75 63 68 20 74 68 61 74 20 65 61 63 68 0a 20 20 20 20 76 65 72 74 65 78 20 .of.G.such.that.each.....vertex.
1060 68 61 73 20 64 65 67 72 65 65 20 6b 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 has.degree.k.......Parameters...
1080 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 6f 72 6b 58 20 67 72 ..----------.....G.:.NetworkX.gr
10a0 61 70 68 0a 20 20 20 20 20 20 55 6e 64 69 72 65 63 74 65 64 20 67 72 61 70 68 0a 0a 20 20 20 20 aph.......Undirected.graph......
10c0 6d 61 74 63 68 69 6e 67 5f 77 65 69 67 68 74 3a 20 73 74 72 69 6e 67 2c 20 6f 70 74 69 6f 6e 61 matching_weight:.string,.optiona
10e0 6c 20 28 64 65 66 61 75 6c 74 3d 27 77 65 69 67 68 74 27 29 0a 20 20 20 20 20 20 20 45 64 67 65 l.(default='weight')........Edge
1100 20 64 61 74 61 20 6b 65 79 20 63 6f 72 72 65 73 70 6f 6e 64 69 6e 67 20 74 6f 20 74 68 65 20 65 .data.key.corresponding.to.the.e
1120 64 67 65 20 77 65 69 67 68 74 2e 0a 20 20 20 20 20 20 20 55 73 65 64 20 66 6f 72 20 66 69 6e 64 dge.weight.........Used.for.find
1140 69 6e 67 20 74 68 65 20 6d 61 78 2d 77 65 69 67 68 74 65 64 20 70 65 72 66 65 63 74 20 6d 61 74 ing.the.max-weighted.perfect.mat
1160 63 68 69 6e 67 2e 0a 20 20 20 20 20 20 20 49 66 20 6b 65 79 20 6e 6f 74 20 66 6f 75 6e 64 2c 20 ching.........If.key.not.found,.
1180 75 73 65 73 20 31 20 61 73 20 77 65 69 67 68 74 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 uses.1.as.weight.......Returns..
11a0 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 32 20 3a 20 4e 65 74 77 6f 72 6b 58 20 67 72 61 ...-------.....G2.:.NetworkX.gra
11c0 70 68 0a 20 20 20 20 20 20 20 20 41 20 6b 2d 66 61 63 74 6f 72 20 6f 66 20 47 0a 0a 20 20 20 20 ph.........A.k-factor.of.G......
11e0 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 20 Examples.....--------.....>>>.G.
1200 3d 20 6e 78 2e 47 72 61 70 68 28 5b 28 31 2c 20 32 29 2c 20 28 32 2c 20 33 29 2c 20 28 33 2c 20 =.nx.Graph([(1,.2),.(2,.3),.(3,.
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12a0 20 20 20 2e 2e 20 5b 31 5d 20 22 41 6e 20 61 6c 67 6f 72 69 74 68 6d 20 66 6f 72 20 63 6f 6d 70 ......[1]."An.algorithm.for.comp
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12e0 20 4d 65 69 6a 65 72 2c 20 48 65 6e 6b 2c 20 59 75 72 61 69 20 4e c3 ba c3 b1 65 7a 2d 52 6f 64 .Meijer,.Henk,.Yurai.N....ez-Rod
1300 72 c3 ad 67 75 65 7a 2c 20 61 6e 64 20 44 61 76 69 64 20 52 61 70 70 61 70 6f 72 74 2c 0a 20 20 r..guez,.and.David.Rappaport,...
1320 20 20 20 20 20 49 6e 66 6f 72 6d 61 74 69 6f 6e 20 70 72 6f 63 65 73 73 69 6e 67 20 6c 65 74 74 .....Information.processing.lett
1340 65 72 73 2c 20 32 30 30 39 2e 0a 20 20 20 20 72 02 00 00 00 29 02 da 13 69 73 5f 70 65 72 66 65 ers,.2009......r....)...is_perfe
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13a0 5a 01 64 00 5a 02 64 01 84 00 5a 03 64 02 84 00 5a 04 88 00 66 01 64 03 84 08 5a 05 79 04 29 05 Z.d.Z.d...Z.d...Z...f.d...Z.y.).
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