| ofs | hex dump | ascii |
|---|---|---|
| 0000 | cb 0d 0d 0a 00 00 00 00 85 fa a7 68 d7 3d 00 00 e3 00 00 00 00 00 00 00 00 00 00 00 00 03 00 00 | ...........h.=.................. |
| 0020 | 00 00 00 00 00 f3 54 01 00 00 97 00 64 00 5a 00 64 01 64 02 6c 01 5a 01 64 01 64 02 6c 02 5a 03 | ......T.....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 ac 04 ab 01 00 00 00 00 00 00 64 0c 64 05 84 01 ab 00 00 00 00 00 00 00 5a 06 64 06 84 00 | d...........d.d...........Z.d... |
| 0080 | 5a 07 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 02 ac 04 ab 01 | Z...e.j...................d..... |
| 00a0 | 00 00 00 00 00 00 64 07 84 00 ab 00 00 00 00 00 00 00 5a 08 02 00 65 03 6a 0a 00 00 00 00 00 00 | ......d...........Z...e.j....... |
| 00c0 | 00 00 00 00 00 00 00 00 00 00 00 00 64 02 ac 04 ab 01 00 00 00 00 00 00 64 08 84 00 ab 00 00 00 | ............d...........d....... |
| 00e0 | 00 00 00 00 5a 09 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 02 | ....Z...e.j...................d. |
| 0100 | ac 04 ab 01 00 00 00 00 00 00 64 09 84 00 ab 00 00 00 00 00 00 00 5a 0a 02 00 65 03 6a 0a 00 00 | ..........d...........Z...e.j... |
| 0120 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 02 ac 04 ab 01 00 00 00 00 00 00 64 0a 84 00 | ................d...........d... |
| 0140 | ab 00 00 00 00 00 00 00 5a 0b 02 00 65 03 6a 0a 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | ........Z...e.j................. |
| 0160 | 00 00 64 02 ac 04 ab 01 00 00 00 00 00 00 64 0b 84 00 ab 00 00 00 00 00 00 00 5a 0c 79 02 29 0d | ..d...........d...........Z.y.). |
| 0180 | 7a 1e 54 65 73 74 20 73 65 71 75 65 6e 63 65 73 20 66 6f 72 20 67 72 61 70 68 69 6e 65 73 73 2e | z.Test.sequences.for.graphiness. |
| 01a0 | e9 00 00 00 00 4e 29 06 da 0c 69 73 5f 67 72 61 70 68 69 63 61 6c da 11 69 73 5f 6d 75 6c 74 69 | .....N)...is_graphical..is_multi |
| 01c0 | 67 72 61 70 68 69 63 61 6c da 12 69 73 5f 70 73 65 75 64 6f 67 72 61 70 68 69 63 61 6c da 0e 69 | graphical..is_pseudographical..i |
| 01e0 | 73 5f 64 69 67 72 61 70 68 69 63 61 6c da 25 69 73 5f 76 61 6c 69 64 5f 64 65 67 72 65 65 5f 73 | s_digraphical.%is_valid_degree_s |
| 0200 | 65 71 75 65 6e 63 65 5f 65 72 64 6f 73 5f 67 61 6c 6c 61 69 da 25 69 73 5f 76 61 6c 69 64 5f 64 | equence_erdos_gallai.%is_valid_d |
| 0220 | 65 67 72 65 65 5f 73 65 71 75 65 6e 63 65 5f 68 61 76 65 6c 5f 68 61 6b 69 6d 69 29 01 da 06 67 | egree_sequence_havel_hakimi)...g |
| 0240 | 72 61 70 68 73 63 02 00 00 00 00 00 00 00 00 00 00 00 05 00 00 00 03 00 00 00 f3 9c 00 00 00 97 | raphsc.......................... |
| 0260 | 00 7c 01 64 01 6b 28 00 00 72 16 74 01 00 00 00 00 00 00 00 00 74 03 00 00 00 00 00 00 00 00 7c | .|.d.k(..r.t.........t.........| |
| 0280 | 00 ab 01 00 00 00 00 00 00 ab 01 00 00 00 00 00 00 7d 02 7c 02 53 00 7c 01 64 02 6b 28 00 00 72 | .................}.|.S.|.d.k(..r |
| 02a0 | 16 74 05 00 00 00 00 00 00 00 00 74 03 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 ab | .t.........t.........|.......... |
| 02c0 | 01 00 00 00 00 00 00 7d 02 7c 02 53 00 64 03 7d 03 74 07 00 00 00 00 00 00 00 00 6a 08 00 00 00 | .......}.|.S.d.}.t.........j.... |
| 02e0 | 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 29 04 75 73 06 | ...............|...........).us. |
| 0300 | 00 00 52 65 74 75 72 6e 73 20 54 72 75 65 20 69 66 20 73 65 71 75 65 6e 63 65 20 69 73 20 61 20 | ..Returns.True.if.sequence.is.a. |
| 0320 | 76 61 6c 69 64 20 64 65 67 72 65 65 20 73 65 71 75 65 6e 63 65 2e 0a 0a 20 20 20 20 41 20 64 65 | valid.degree.sequence.......A.de |
| 0340 | 67 72 65 65 20 73 65 71 75 65 6e 63 65 20 69 73 20 76 61 6c 69 64 20 69 66 20 73 6f 6d 65 20 67 | gree.sequence.is.valid.if.some.g |
| 0360 | 72 61 70 68 20 63 61 6e 20 72 65 61 6c 69 7a 65 20 69 74 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 | raph.can.realize.it.......Parame |
| 0380 | 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 73 65 71 75 65 6e 63 65 | ters.....----------.....sequence |
| 03a0 | 20 3a 20 6c 69 73 74 20 6f 72 20 69 74 65 72 61 62 6c 65 20 63 6f 6e 74 61 69 6e 65 72 0a 20 20 | .:.list.or.iterable.container... |
| 03c0 | 20 20 20 20 20 20 41 20 73 65 71 75 65 6e 63 65 20 6f 66 20 69 6e 74 65 67 65 72 20 6e 6f 64 65 | ......A.sequence.of.integer.node |
| 03e0 | 20 64 65 67 72 65 65 73 0a 0a 20 20 20 20 6d 65 74 68 6f 64 20 3a 20 22 65 67 22 20 7c 20 22 68 | .degrees......method.:."eg".|."h |
| 0400 | 68 22 20 20 28 64 65 66 61 75 6c 74 3a 20 27 65 67 27 29 0a 20 20 20 20 20 20 20 20 54 68 65 20 | h"..(default:.'eg').........The. |
| 0420 | 6d 65 74 68 6f 64 20 75 73 65 64 20 74 6f 20 76 61 6c 69 64 61 74 65 20 74 68 65 20 64 65 67 72 | method.used.to.validate.the.degr |
| 0440 | 65 65 20 73 65 71 75 65 6e 63 65 2e 0a 20 20 20 20 20 20 20 20 22 65 67 22 20 63 6f 72 72 65 73 | ee.sequence.........."eg".corres |
| 0460 | 70 6f 6e 64 73 20 74 6f 20 74 68 65 20 45 72 64 c5 91 73 2d 47 61 6c 6c 61 69 20 61 6c 67 6f 72 | ponds.to.the.Erd..s-Gallai.algor |
| 0480 | 69 74 68 6d 0a 20 20 20 20 20 20 20 20 5b 45 47 31 39 36 30 5d 5f 2c 20 5b 63 68 6f 75 64 75 6d | ithm.........[EG1960]_,.[choudum |
| 04a0 | 31 39 38 36 5d 5f 2c 20 61 6e 64 0a 20 20 20 20 20 20 20 20 22 68 68 22 20 74 6f 20 74 68 65 20 | 1986]_,.and........."hh".to.the. |
| 04c0 | 48 61 76 65 6c 2d 48 61 6b 69 6d 69 20 61 6c 67 6f 72 69 74 68 6d 0a 20 20 20 20 20 20 20 20 5b | Havel-Hakimi.algorithm.........[ |
| 04e0 | 68 61 76 65 6c 31 39 35 35 5d 5f 2c 20 5b 68 61 6b 69 6d 69 31 39 36 32 5d 5f 2c 20 5b 43 4c 31 | havel1955]_,.[hakimi1962]_,.[CL1 |
| 0500 | 39 39 36 5d 5f 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 | 996]_.......Returns.....-------. |
| 0520 | 20 20 20 20 76 61 6c 69 64 20 3a 20 62 6f 6f 6c 0a 20 20 20 20 20 20 20 20 54 72 75 65 20 69 66 | ....valid.:.bool.........True.if |
| 0540 | 20 74 68 65 20 73 65 71 75 65 6e 63 65 20 69 73 20 61 20 76 61 6c 69 64 20 64 65 67 72 65 65 20 | .the.sequence.is.a.valid.degree. |
| 0560 | 73 65 71 75 65 6e 63 65 20 61 6e 64 20 46 61 6c 73 65 20 69 66 20 6e 6f 74 2e 0a 0a 20 20 20 20 | sequence.and.False.if.not....... |
| 0580 | 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. |
| 05a0 | 3d 20 6e 78 2e 70 61 74 68 5f 67 72 61 70 68 28 34 29 0a 20 20 20 20 3e 3e 3e 20 73 65 71 75 65 | =.nx.path_graph(4).....>>>.seque |
| 05c0 | 6e 63 65 20 3d 20 28 64 20 66 6f 72 20 6e 2c 20 64 20 69 6e 20 47 2e 64 65 67 72 65 65 28 29 29 | nce.=.(d.for.n,.d.in.G.degree()) |
| 05e0 | 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 69 73 5f 67 72 61 70 68 69 63 61 6c 28 73 65 71 75 65 6e 63 | .....>>>.nx.is_graphical(sequenc |
| 0600 | 65 29 0a 20 20 20 20 54 72 75 65 0a 0a 20 20 20 20 54 6f 20 74 65 73 74 20 61 20 6e 6f 6e 2d 67 | e).....True......To.test.a.non-g |
| 0620 | 72 61 70 68 69 63 61 6c 20 73 65 71 75 65 6e 63 65 3a 0a 20 20 20 20 3e 3e 3e 20 73 65 71 75 65 | raphical.sequence:.....>>>.seque |
| 0640 | 6e 63 65 5f 6c 69 73 74 20 3d 20 5b 64 20 66 6f 72 20 6e 2c 20 64 20 69 6e 20 47 2e 64 65 67 72 | nce_list.=.[d.for.n,.d.in.G.degr |
| 0660 | 65 65 28 29 5d 0a 20 20 20 20 3e 3e 3e 20 73 65 71 75 65 6e 63 65 5f 6c 69 73 74 5b 2d 31 5d 20 | ee()].....>>>.sequence_list[-1]. |
| 0680 | 2b 3d 20 31 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 69 73 5f 67 72 61 70 68 69 63 61 6c 28 73 65 71 | +=.1.....>>>.nx.is_graphical(seq |
| 06a0 | 75 65 6e 63 65 5f 6c 69 73 74 29 0a 20 20 20 20 46 61 6c 73 65 0a 0a 20 20 20 20 52 65 66 65 72 | uence_list).....False......Refer |
| 06c0 | 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 45 47 31 | ences.....----------........[EG1 |
| 06e0 | 39 36 30 5d 20 45 72 64 c5 91 73 20 61 6e 64 20 47 61 6c 6c 61 69 2c 20 4d 61 74 2e 20 4c 61 70 | 960].Erd..s.and.Gallai,.Mat..Lap |
| 0700 | 6f 6b 20 31 31 20 32 36 34 2c 20 31 39 36 30 2e 0a 20 20 20 20 2e 2e 20 5b 63 68 6f 75 64 75 6d | ok.11.264,.1960.........[choudum |
| 0720 | 31 39 38 36 5d 20 53 2e 41 2e 20 43 68 6f 75 64 75 6d 2e 20 22 41 20 73 69 6d 70 6c 65 20 70 72 | 1986].S.A..Choudum.."A.simple.pr |
| 0740 | 6f 6f 66 20 6f 66 20 74 68 65 20 45 72 64 c5 91 73 2d 47 61 6c 6c 61 69 20 74 68 65 6f 72 65 6d | oof.of.the.Erd..s-Gallai.theorem |
| 0760 | 20 6f 6e 0a 20 20 20 20 20 20 20 67 72 61 70 68 20 73 65 71 75 65 6e 63 65 73 2e 22 20 42 75 6c | .on........graph.sequences.".Bul |
| 0780 | 6c 65 74 69 6e 20 6f 66 20 74 68 65 20 41 75 73 74 72 61 6c 69 61 6e 20 4d 61 74 68 65 6d 61 74 | letin.of.the.Australian.Mathemat |
| 07a0 | 69 63 61 6c 20 53 6f 63 69 65 74 79 2c 20 33 33 2c 0a 20 20 20 20 20 20 20 70 70 20 36 37 2d 37 | ical.Society,.33,........pp.67-7 |
| 07c0 | 30 2c 20 31 39 38 36 2e 20 68 74 74 70 73 3a 2f 2f 64 6f 69 2e 6f 72 67 2f 31 30 2e 31 30 31 37 | 0,.1986..https://doi.org/10.1017 |
| 07e0 | 2f 53 30 30 30 34 39 37 32 37 30 30 30 30 32 38 37 32 0a 20 20 20 20 2e 2e 20 5b 68 61 76 65 6c | /S0004972700002872........[havel |
| 0800 | 31 39 35 35 5d 20 48 61 76 65 6c 2c 20 56 2e 20 22 41 20 52 65 6d 61 72 6b 20 6f 6e 20 74 68 65 | 1955].Havel,.V.."A.Remark.on.the |
| 0820 | 20 45 78 69 73 74 65 6e 63 65 20 6f 66 20 46 69 6e 69 74 65 20 47 72 61 70 68 73 22 0a 20 20 20 | .Existence.of.Finite.Graphs".... |
| 0840 | 20 20 20 20 43 61 73 6f 70 69 73 20 50 65 73 74 2e 20 4d 61 74 2e 20 38 30 2c 20 34 37 37 2d 34 | ....Casopis.Pest..Mat..80,.477-4 |
| 0860 | 38 30 2c 20 31 39 35 35 2e 0a 20 20 20 20 2e 2e 20 5b 68 61 6b 69 6d 69 31 39 36 32 5d 20 48 61 | 80,.1955.........[hakimi1962].Ha |
| 0880 | 6b 69 6d 69 2c 20 53 2e 20 22 4f 6e 20 74 68 65 20 52 65 61 6c 69 7a 61 62 69 6c 69 74 79 20 6f | kimi,.S.."On.the.Realizability.o |
| 08a0 | 66 20 61 20 53 65 74 20 6f 66 20 49 6e 74 65 67 65 72 73 20 61 73 0a 20 20 20 20 20 20 20 44 65 | f.a.Set.of.Integers.as........De |
| 08c0 | 67 72 65 65 73 20 6f 66 20 74 68 65 20 56 65 72 74 69 63 65 73 20 6f 66 20 61 20 47 72 61 70 68 | grees.of.the.Vertices.of.a.Graph |
| 08e0 | 2e 22 20 53 49 41 4d 20 4a 2e 20 41 70 70 6c 2e 20 4d 61 74 68 2e 20 31 30 2c 20 34 39 36 2d 35 | .".SIAM.J..Appl..Math..10,.496-5 |
| 0900 | 30 36 2c 20 31 39 36 32 2e 0a 20 20 20 20 2e 2e 20 5b 43 4c 31 39 39 36 5d 20 47 2e 20 43 68 61 | 06,.1962.........[CL1996].G..Cha |
| 0920 | 72 74 72 61 6e 64 20 61 6e 64 20 4c 2e 20 4c 65 73 6e 69 61 6b 2c 20 22 47 72 61 70 68 73 20 61 | rtrand.and.L..Lesniak,."Graphs.a |
| 0940 | 6e 64 20 44 69 67 72 61 70 68 73 22 2c 0a 20 20 20 20 20 20 20 43 68 61 70 6d 61 6e 20 61 6e 64 | nd.Digraphs",........Chapman.and |
| 0960 | 20 48 61 6c 6c 2f 43 52 43 2c 20 31 39 39 36 2e 0a 20 20 20 20 da 02 65 67 da 02 68 68 7a 1d 60 | .Hall/CRC,.1996........eg..hhz.` |
| 0980 | 6d 65 74 68 6f 64 60 20 6d 75 73 74 20 62 65 20 27 65 67 27 20 6f 72 20 27 68 68 27 29 05 72 07 | method`.must.be.'eg'.or.'hh').r. |
| 09a0 | 00 00 00 da 04 6c 69 73 74 72 08 00 00 00 da 02 6e 78 da 11 4e 65 74 77 6f 72 6b 58 45 78 63 65 | .....listr......nx..NetworkXExce |
| 09c0 | 70 74 69 6f 6e 29 04 da 08 73 65 71 75 65 6e 63 65 da 06 6d 65 74 68 6f 64 da 05 76 61 6c 69 64 | ption)...sequence..method..valid |
| 09e0 | da 03 6d 73 67 73 04 00 00 00 20 20 20 20 fa 64 2f 68 6f 6d 65 2f 62 6c 61 63 6b 68 61 6f 2f 75 | ..msgs.........d/home/blackhao/u |
| 0a00 | 69 75 63 2d 63 6f 75 72 73 65 2d 67 72 61 70 68 2f 2e 76 65 6e 76 2f 6c 69 62 2f 70 79 74 68 6f | iuc-course-graph/.venv/lib/pytho |
| 0a20 | 6e 33 2e 31 32 2f 73 69 74 65 2d 70 61 63 6b 61 67 65 73 2f 6e 65 74 77 6f 72 6b 78 2f 61 6c 67 | n3.12/site-packages/networkx/alg |
| 0a40 | 6f 72 69 74 68 6d 73 2f 67 72 61 70 68 69 63 61 6c 2e 70 79 72 03 00 00 00 72 03 00 00 00 11 00 | orithms/graphical.pyr....r...... |
| 0a60 | 00 00 73 57 00 00 00 80 00 f0 62 01 00 08 0e 90 14 82 7e dc 10 35 b4 64 b8 38 b3 6e d3 10 45 88 | ..sW......b.......~..5.d.8.n..E. |
| 0a80 | 05 f0 0c 00 0c 11 80 4c f0 0b 00 0a 10 90 34 8a 1e dc 10 35 b4 64 b8 38 b3 6e d3 10 45 88 05 f0 | .......L......4....5.d.8.n..E... |
| 0aa0 | 08 00 0c 11 80 4c f0 05 00 0f 2e 88 03 dc 0e 10 d7 0e 22 d1 0e 22 a0 33 d3 0e 27 d0 08 27 f3 00 | .....L............"..".3..'..'.. |
| 0ac0 | 00 00 00 63 01 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 03 00 00 00 f3 78 01 00 00 97 00 74 | ...c.....................x.....t |
| 0ae0 | 00 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 6a 05 00 | .........j...................j.. |
| 0b00 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 7d 00 74 07 00 | .................|.........}.t.. |
| 0b20 | 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 7d 01 64 01 67 01 7c 01 7a 05 00 00 7d 02 64 | .......|.........}.d.g.|.z...}.d |
| 0b40 | 01 7c 01 64 01 64 01 66 04 5c 04 00 00 7d 03 7d 04 7d 05 7d 06 7c 00 44 00 5d 54 00 00 7d 07 7c | .|.d.d.f.\...}.}.}.}.|.D.]T..}.| |
| 0b60 | 07 64 01 6b 02 00 00 73 05 7c 07 7c 01 6b 5c 00 00 72 10 74 00 00 00 00 00 00 00 00 00 6a 08 00 | .d.k...s.|.|.k\..r.t.........j.. |
| 0b80 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 82 01 7c 07 64 01 6b 44 00 00 73 01 8c 23 74 | ...................|.d.kD..s..#t |
| 0ba0 | 0b 00 00 00 00 00 00 00 00 7c 03 7c 07 ab 02 00 00 00 00 00 00 74 0d 00 00 00 00 00 00 00 00 7c | .........|.|.........t.........| |
| 0bc0 | 04 7c 07 ab 02 00 00 00 00 00 00 7c 05 7c 07 7a 00 00 00 7c 06 64 02 7a 00 00 00 66 04 5c 04 00 | .|.........|.|.z...|.d.z...f.\.. |
| 0be0 | 00 7d 03 7d 04 7d 05 7d 06 7c 02 7c 07 78 02 78 02 19 00 00 00 64 02 7a 0d 00 00 63 03 63 02 3c | .}.}.}.}.|.|.x.x.....d.z...c.c.< |
| 0c00 | 00 00 00 8c 56 04 00 7c 05 64 03 7a 06 00 00 73 0b 7c 05 7c 06 7c 06 64 02 7a 0a 00 00 7a 05 00 | ....V..|.d.z...s.|.|.|.d.z...z.. |
| 0c20 | 00 6b 44 00 00 72 10 74 00 00 00 00 00 00 00 00 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 00 | .kD..r.t.........j.............. |
| 0c40 | 00 00 00 00 00 82 01 7c 03 7c 04 7c 05 7c 06 7c 02 66 05 53 00 29 04 4e 72 02 00 00 00 e9 01 00 | .......|.|.|.|.|.f.S.).Nr....... |
| 0c60 | 00 00 e9 02 00 00 00 29 07 72 0e 00 00 00 da 05 75 74 69 6c 73 da 11 6d 61 6b 65 5f 6c 69 73 74 | .......).r......utils..make_list |
| 0c80 | 5f 6f 66 5f 69 6e 74 73 da 03 6c 65 6e da 12 4e 65 74 77 6f 72 6b 58 55 6e 66 65 61 73 69 62 6c | _of_ints..len..NetworkXUnfeasibl |
| 0ca0 | 65 da 03 6d 61 78 da 03 6d 69 6e 29 08 da 0c 64 65 67 5f 73 65 71 75 65 6e 63 65 da 01 70 da 08 | e..max..min)...deg_sequence..p.. |
| 0cc0 | 6e 75 6d 5f 64 65 67 73 da 04 64 6d 61 78 da 04 64 6d 69 6e da 04 64 73 75 6d da 01 6e da 01 64 | num_degs..dmax..dmin..dsum..n..d |
| 0ce0 | 73 08 00 00 00 20 20 20 20 20 20 20 20 72 14 00 00 00 da 16 5f 62 61 73 69 63 5f 67 72 61 70 68 | s............r......_basic_graph |
| 0d00 | 69 63 61 6c 5f 74 65 73 74 73 72 27 00 00 00 4c 00 00 00 73 de 00 00 00 80 00 e4 13 15 97 38 91 | ical_testsr'...L...s..........8. |
| 0d20 | 38 d7 13 2d d1 13 2d a8 6c d3 13 3b 80 4c dc 08 0b 88 4c d3 08 19 80 41 d8 10 11 88 73 90 51 89 | 8..-..-.l..;.L....L....A....s.Q. |
| 0d40 | 77 80 48 d8 1a 1b 98 51 a0 01 a0 31 98 2a d1 04 17 80 44 88 24 90 04 90 61 d8 0d 19 f2 00 07 05 | w.H....Q...1.*....D.$...a....... |
| 0d60 | 1d 88 01 e0 0b 0c 88 71 8a 35 90 41 98 11 92 46 dc 12 14 d7 12 27 d1 12 27 d0 0c 27 e0 0d 0e 90 | .......q.5.A...F.....'..'..'.... |
| 0d80 | 11 8b 55 dc 22 25 a0 64 a8 41 a3 2c b4 03 b0 44 b8 21 b3 0c b8 64 c0 51 b9 68 c8 01 c8 41 c9 05 | ..U."%.d.A.,...D.!...d.Q.h...A.. |
| 0da0 | d0 22 4d d1 0c 1f 88 44 90 24 98 04 98 61 d8 0c 14 90 51 8b 4b 98 31 d1 0c 1c 8c 4b f0 0f 07 05 | ."M....D.$...a....Q.K.1....K.... |
| 0dc0 | 1d f0 12 00 08 0c 88 61 82 78 90 34 98 21 98 71 a0 31 99 75 99 2b d2 13 25 dc 0e 10 d7 0e 23 d1 | .......a.x.4.!.q.1.u.+..%.....#. |
| 0de0 | 0e 23 d0 08 23 d8 0b 0f 90 14 90 74 98 51 a0 08 d0 0b 28 d0 04 28 72 15 00 00 00 63 01 00 00 00 | .#..#......t.Q....(..(r....c.... |
| 0e00 | 00 00 00 00 00 00 00 00 05 00 00 00 03 00 00 00 f3 0a 02 00 00 97 00 09 00 74 01 00 00 00 00 00 | .........................t...... |
| 0e20 | 00 00 00 7c 00 ab 01 00 00 00 00 00 00 5c 05 00 00 7d 01 7d 02 7d 03 7d 04 7d 05 7c 04 64 02 6b | ...|.........\...}.}.}.}.}.|.d.k |
| 0e40 | 28 00 00 73 1a 64 03 7c 02 7a 05 00 00 7c 04 7a 05 00 00 7c 01 7c 02 7a 00 00 00 64 04 7a 00 00 | (..s.d.|.z...|.z...|.|.z...d.z.. |
| 0e60 | 00 7c 01 7c 02 7a 00 00 00 64 04 7a 00 00 00 7a 05 00 00 6b 5c 00 00 72 01 79 05 64 02 67 01 7c | .|.|.z...d.z...z...k\..r.y.d.g.| |
| 0e80 | 01 64 04 7a 00 00 00 7a 05 00 00 7d 06 7c 04 64 02 6b 44 00 00 72 aa 7c 05 7c 01 19 00 00 00 64 | .d.z...z...}.|.d.kD..r.|.|.....d |
| 0ea0 | 02 6b 28 00 00 72 0e 7c 01 64 04 7a 17 00 00 7d 01 7c 05 7c 01 19 00 00 00 64 02 6b 28 00 00 72 | .k(..r.|.d.z...}.|.|.....d.k(..r |
| 0ec0 | 01 8c 0e 7c 01 7c 04 64 04 7a 0a 00 00 6b 44 00 00 72 01 79 01 7c 05 7c 01 19 00 00 00 64 04 7a | ...|.|.d.z...kD..r.y.|.|.....d.z |
| 0ee0 | 0a 00 00 7c 04 64 04 7a 0a 00 00 63 02 7c 05 7c 01 3c 00 00 00 7d 04 64 02 7d 07 7c 01 7d 08 74 | ...|.d.z...c.|.|.<...}.d.}.|.}.t |
| 0f00 | 07 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 44 00 5d 3c 00 00 7d 09 7c 05 7c 08 19 | .........|.........D.]<..}.|.|.. |
| 0f20 | 00 00 00 64 02 6b 28 00 00 72 0e 7c 08 64 04 7a 17 00 00 7d 08 7c 05 7c 08 19 00 00 00 64 02 6b | ...d.k(..r.|.d.z...}.|.|.....d.k |
| 0f40 | 28 00 00 72 01 8c 0e 7c 05 7c 08 19 00 00 00 64 04 7a 0a 00 00 7c 04 64 04 7a 0a 00 00 63 02 7c | (..r...|.|.....d.z...|.d.z...c.| |
| 0f60 | 05 7c 08 3c 00 00 00 7d 04 7c 08 64 04 6b 44 00 00 73 01 8c 30 7c 08 64 04 7a 0a 00 00 7c 06 7c | .|.<...}.|.d.kD..s..0|.d.z...|.| |
| 0f80 | 07 3c 00 00 00 7c 07 64 04 7a 0d 00 00 7d 07 8c 3e 04 00 74 07 00 00 00 00 00 00 00 00 7c 07 ab | .<...|.d.z...}..>..t.........|.. |
| 0fa0 | 01 00 00 00 00 00 00 44 00 5d 18 00 00 7d 09 7c 06 7c 09 19 00 00 00 7d 0a 7c 05 7c 0a 19 00 00 | .......D.]...}.|.|.....}.|.|.... |
| 0fc0 | 00 64 04 7a 00 00 00 7c 04 64 04 7a 00 00 00 63 02 7c 05 7c 0a 3c 00 00 00 7d 04 8c 1a 04 00 7c | .d.z...|.d.z...c.|.|.<...}.....| |
| 0fe0 | 04 64 02 6b 44 00 00 72 01 8c aa 79 05 23 00 74 02 00 00 00 00 00 00 00 00 6a 04 00 00 00 00 00 | .d.kD..r...y.#.t.........j...... |
| 1000 | 00 00 00 00 00 00 00 00 00 00 00 00 00 24 00 72 03 01 00 59 00 79 01 77 00 78 03 59 00 77 01 29 | .............$.r...Y.y.w.x.Y.w.) |
| 1020 | 06 61 96 06 00 00 52 65 74 75 72 6e 73 20 54 72 75 65 20 69 66 20 64 65 67 5f 73 65 71 75 65 6e | .a....Returns.True.if.deg_sequen |
| 1040 | 63 65 20 63 61 6e 20 62 65 20 72 65 61 6c 69 7a 65 64 20 62 79 20 61 20 73 69 6d 70 6c 65 20 67 | ce.can.be.realized.by.a.simple.g |
| 1060 | 72 61 70 68 2e 0a 0a 20 20 20 20 54 68 65 20 76 61 6c 69 64 61 74 69 6f 6e 20 70 72 6f 63 65 65 | raph.......The.validation.procee |
| 1080 | 64 73 20 75 73 69 6e 67 20 74 68 65 20 48 61 76 65 6c 2d 48 61 6b 69 6d 69 20 74 68 65 6f 72 65 | ds.using.the.Havel-Hakimi.theore |
| 10a0 | 6d 0a 20 20 20 20 5b 68 61 76 65 6c 31 39 35 35 5d 5f 2c 20 5b 68 61 6b 69 6d 69 31 39 36 32 5d | m.....[havel1955]_,.[hakimi1962] |
| 10c0 | 5f 2c 20 5b 43 4c 31 39 39 36 5d 5f 2e 0a 20 20 20 20 57 6f 72 73 74 2d 63 61 73 65 20 72 75 6e | _,.[CL1996]_......Worst-case.run |
| 10e0 | 20 74 69 6d 65 20 69 73 20 24 4f 28 73 29 24 20 77 68 65 72 65 20 24 73 24 20 69 73 20 74 68 65 | .time.is.$O(s)$.where.$s$.is.the |
| 1100 | 20 73 75 6d 20 6f 66 20 74 68 65 20 73 65 71 75 65 6e 63 65 2e 0a 0a 20 20 20 20 50 61 72 61 6d | .sum.of.the.sequence.......Param |
| 1120 | 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 64 65 67 5f 73 65 71 | eters.....----------.....deg_seq |
| 1140 | 75 65 6e 63 65 20 3a 20 6c 69 73 74 0a 20 20 20 20 20 20 20 20 41 20 6c 69 73 74 20 6f 66 20 69 | uence.:.list.........A.list.of.i |
| 1160 | 6e 74 65 67 65 72 73 20 77 68 65 72 65 20 65 61 63 68 20 65 6c 65 6d 65 6e 74 20 73 70 65 63 69 | ntegers.where.each.element.speci |
| 1180 | 66 69 65 73 20 74 68 65 20 64 65 67 72 65 65 20 6f 66 20 61 20 6e 6f 64 65 0a 20 20 20 20 20 20 | fies.the.degree.of.a.node....... |
| 11a0 | 20 20 69 6e 20 61 20 67 72 61 70 68 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d | ..in.a.graph.......Returns.....- |
| 11c0 | 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 76 61 6c 69 64 20 3a 20 62 6f 6f 6c 0a 20 20 20 20 20 20 20 20 | ------.....valid.:.bool......... |
| 11e0 | 54 72 75 65 20 69 66 20 64 65 67 5f 73 65 71 75 65 6e 63 65 20 69 73 20 67 72 61 70 68 69 63 61 | True.if.deg_sequence.is.graphica |
| 1200 | 6c 20 61 6e 64 20 46 61 6c 73 65 20 69 66 20 6e 6f 74 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 | l.and.False.if.not.......Example |
| 1220 | 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 47 72 | s.....--------.....>>>.G.=.nx.Gr |
| 1240 | 61 70 68 28 5b 28 31 2c 20 32 29 2c 20 28 31 2c 20 33 29 2c 20 28 32 2c 20 33 29 2c 20 28 33 2c | aph([(1,.2),.(1,.3),.(2,.3),.(3, |
| 1260 | 20 34 29 2c 20 28 34 2c 20 32 29 2c 20 28 35 2c 20 31 29 2c 20 28 35 2c 20 34 29 5d 29 0a 20 20 | .4),.(4,.2),.(5,.1),.(5,.4)])... |
| 1280 | 20 20 3e 3e 3e 20 73 65 71 75 65 6e 63 65 20 3d 20 28 64 20 66 6f 72 20 5f 2c 20 64 20 69 6e 20 | ..>>>.sequence.=.(d.for._,.d.in. |
| 12a0 | 47 2e 64 65 67 72 65 65 28 29 29 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 69 73 5f 76 61 6c 69 64 5f | G.degree()).....>>>.nx.is_valid_ |
| 12c0 | 64 65 67 72 65 65 5f 73 65 71 75 65 6e 63 65 5f 68 61 76 65 6c 5f 68 61 6b 69 6d 69 28 73 65 71 | degree_sequence_havel_hakimi(seq |
| 12e0 | 75 65 6e 63 65 29 0a 20 20 20 20 54 72 75 65 0a 0a 20 20 20 20 54 6f 20 74 65 73 74 20 61 20 6e | uence).....True......To.test.a.n |
| 1300 | 6f 6e 2d 76 61 6c 69 64 20 73 65 71 75 65 6e 63 65 3a 0a 20 20 20 20 3e 3e 3e 20 73 65 71 75 65 | on-valid.sequence:.....>>>.seque |
| 1320 | 6e 63 65 5f 6c 69 73 74 20 3d 20 5b 64 20 66 6f 72 20 5f 2c 20 64 20 69 6e 20 47 2e 64 65 67 72 | nce_list.=.[d.for._,.d.in.G.degr |
| 1340 | 65 65 28 29 5d 0a 20 20 20 20 3e 3e 3e 20 73 65 71 75 65 6e 63 65 5f 6c 69 73 74 5b 2d 31 5d 20 | ee()].....>>>.sequence_list[-1]. |
| 1360 | 2b 3d 20 31 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 69 73 5f 76 61 6c 69 64 5f 64 65 67 72 65 65 5f | +=.1.....>>>.nx.is_valid_degree_ |
| 1380 | 73 65 71 75 65 6e 63 65 5f 68 61 76 65 6c 5f 68 61 6b 69 6d 69 28 73 65 71 75 65 6e 63 65 5f 6c | sequence_havel_hakimi(sequence_l |
| 13a0 | 69 73 74 29 0a 20 20 20 20 46 61 6c 73 65 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d | ist).....False......Notes.....-- |
| 13c0 | 2d 2d 2d 0a 20 20 20 20 54 68 65 20 5a 5a 20 63 6f 6e 64 69 74 69 6f 6e 20 73 61 79 73 20 74 68 | ---.....The.ZZ.condition.says.th |
| 13e0 | 61 74 20 66 6f 72 20 74 68 65 20 73 65 71 75 65 6e 63 65 20 64 20 69 66 0a 0a 20 20 20 20 2e 2e | at.for.the.sequence.d.if........ |
| 1400 | 20 6d 61 74 68 3a 3a 0a 20 20 20 20 20 20 20 20 7c 64 7c 20 3e 3d 20 5c 66 72 61 63 7b 28 5c 6d | .math::.........|d|.>=.\frac{(\m |
| 1420 | 61 78 28 64 29 20 2b 20 5c 6d 69 6e 28 64 29 20 2b 20 31 29 5e 32 7d 7b 34 2a 5c 6d 69 6e 28 64 | ax(d).+.\min(d).+.1)^2}{4*\min(d |
| 1440 | 29 7d 0a 0a 20 20 20 20 74 68 65 6e 20 64 20 69 73 20 67 72 61 70 68 69 63 61 6c 2e 20 20 54 68 | )}......then.d.is.graphical...Th |
| 1460 | 69 73 20 77 61 73 20 73 68 6f 77 6e 20 69 6e 20 54 68 65 6f 72 65 6d 20 36 20 69 6e 20 5b 31 5d | is.was.shown.in.Theorem.6.in.[1] |
| 1480 | 5f 2e 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d | _.......References.....--------- |
| 14a0 | 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 49 2e 45 2e 20 5a 76 65 72 6f 76 69 63 68 20 61 6e 64 20 | -........[1].I.E..Zverovich.and. |
| 14c0 | 56 2e 45 2e 20 5a 76 65 72 6f 76 69 63 68 2e 20 22 43 6f 6e 74 72 69 62 75 74 69 6f 6e 73 20 74 | V.E..Zverovich.."Contributions.t |
| 14e0 | 6f 20 74 68 65 20 74 68 65 6f 72 79 0a 20 20 20 20 20 20 20 6f 66 20 67 72 61 70 68 69 63 20 73 | o.the.theory........of.graphic.s |
| 1500 | 65 71 75 65 6e 63 65 73 22 2c 20 44 69 73 63 72 65 74 65 20 4d 61 74 68 65 6d 61 74 69 63 73 2c | equences",.Discrete.Mathematics, |
| 1520 | 20 31 30 35 2c 20 70 70 2e 20 32 39 32 2d 33 30 33 20 28 31 39 39 32 29 2e 0a 20 20 20 20 2e 2e | .105,.pp..292-303.(1992)........ |
| 1540 | 20 5b 68 61 76 65 6c 31 39 35 35 5d 20 48 61 76 65 6c 2c 20 56 2e 20 22 41 20 52 65 6d 61 72 6b | .[havel1955].Havel,.V.."A.Remark |
| 1560 | 20 6f 6e 20 74 68 65 20 45 78 69 73 74 65 6e 63 65 20 6f 66 20 46 69 6e 69 74 65 20 47 72 61 70 | .on.the.Existence.of.Finite.Grap |
| 1580 | 68 73 22 0a 20 20 20 20 20 20 20 43 61 73 6f 70 69 73 20 50 65 73 74 2e 20 4d 61 74 2e 20 38 30 | hs"........Casopis.Pest..Mat..80 |
| 15a0 | 2c 20 34 37 37 2d 34 38 30 2c 20 31 39 35 35 2e 0a 20 20 20 20 2e 2e 20 5b 68 61 6b 69 6d 69 31 | ,.477-480,.1955.........[hakimi1 |
| 15c0 | 39 36 32 5d 20 48 61 6b 69 6d 69 2c 20 53 2e 20 22 4f 6e 20 74 68 65 20 52 65 61 6c 69 7a 61 62 | 962].Hakimi,.S.."On.the.Realizab |
| 15e0 | 69 6c 69 74 79 20 6f 66 20 61 20 53 65 74 20 6f 66 20 49 6e 74 65 67 65 72 73 20 61 73 0a 20 20 | ility.of.a.Set.of.Integers.as... |
| 1600 | 20 20 20 20 20 44 65 67 72 65 65 73 20 6f 66 20 74 68 65 20 56 65 72 74 69 63 65 73 20 6f 66 20 | .....Degrees.of.the.Vertices.of. |
| 1620 | 61 20 47 72 61 70 68 2e 22 20 53 49 41 4d 20 4a 2e 20 41 70 70 6c 2e 20 4d 61 74 68 2e 20 31 30 | a.Graph.".SIAM.J..Appl..Math..10 |
| 1640 | 2c 20 34 39 36 2d 35 30 36 2c 20 31 39 36 32 2e 0a 20 20 20 20 2e 2e 20 5b 43 4c 31 39 39 36 5d | ,.496-506,.1962.........[CL1996] |
| 1660 | 20 47 2e 20 43 68 61 72 74 72 61 6e 64 20 61 6e 64 20 4c 2e 20 4c 65 73 6e 69 61 6b 2c 20 22 47 | .G..Chartrand.and.L..Lesniak,."G |
| 1680 | 72 61 70 68 73 20 61 6e 64 20 44 69 67 72 61 70 68 73 22 2c 0a 20 20 20 20 20 20 20 43 68 61 70 | raphs.and.Digraphs",........Chap |
| 16a0 | 6d 61 6e 20 61 6e 64 20 48 61 6c 6c 2f 43 52 43 2c 20 31 39 39 36 2e 0a 20 20 20 20 46 72 02 00 | man.and.Hall/CRC,.1996......Fr.. |
| 16c0 | 00 00 e9 04 00 00 00 72 17 00 00 00 54 a9 04 72 27 00 00 00 72 0e 00 00 00 72 1c 00 00 00 da 05 | .......r....T..r'...r....r...... |
| 16e0 | 72 61 6e 67 65 29 0b 72 1f 00 00 00 72 22 00 00 00 72 23 00 00 00 72 24 00 00 00 72 25 00 00 00 | range).r....r"...r#...r$...r%... |
| 1700 | 72 21 00 00 00 da 08 6d 6f 64 73 74 75 62 73 da 05 6d 73 6c 65 6e da 01 6b da 01 69 da 04 73 74 | r!.....modstubs..mslen..k..i..st |
| 1720 | 75 62 73 0b 00 00 00 20 20 20 20 20 20 20 20 20 20 20 72 14 00 00 00 72 08 00 00 00 72 08 00 00 | ubs...............r....r....r... |
| 1740 | 00 60 00 00 00 73 92 01 00 00 80 00 f0 68 01 03 05 15 dc 28 3e b8 7c d3 28 4c d1 08 25 88 04 88 | .`...s.......h.....(>.|.(L..%... |
| 1760 | 64 90 44 98 21 98 58 f0 08 00 08 09 88 41 82 76 90 11 90 54 91 18 98 41 91 1c a0 24 a8 14 a1 2b | d.D.!.X......A.v...T...A...$...+ |
| 1780 | b0 01 a1 2f b0 64 b8 54 b1 6b c0 41 b1 6f d1 21 46 d2 11 46 d8 0f 13 e0 10 11 88 73 90 64 98 51 | .../.d.T.k.A.o.!F..F.......s.d.Q |
| 17a0 | 91 68 d1 0f 1f 80 48 e0 0a 0b 88 61 8a 25 e0 0e 16 90 74 89 6e a0 01 d2 0e 21 d8 0c 10 90 41 89 | .h....H....a.%....t.n....!....A. |
| 17c0 | 49 88 44 f0 03 00 0f 17 90 74 89 6e a0 01 d3 0e 21 f0 08 00 0c 10 90 21 90 61 91 25 8a 3c d8 13 | I.D......t.n....!......!.a.%.<.. |
| 17e0 | 18 f0 06 00 1d 25 a0 54 99 4e a8 51 d1 1c 2e b0 01 b0 41 b1 05 d0 08 19 88 08 90 14 89 0e 98 01 | .....%.T.N.Q......A............. |
| 1800 | e0 10 11 88 05 d8 0c 10 88 01 dc 11 16 90 74 93 1b f2 00 06 09 1b 88 41 d8 12 1a 98 31 91 2b a0 | ..............t........A....1.+. |
| 1820 | 11 d2 12 22 d8 10 11 90 51 91 06 90 01 f0 03 00 13 1b 98 31 91 2b a0 11 d3 12 22 e0 1d 25 a0 61 | ..."....Q..........1.+...."..%.a |
| 1840 | 99 5b a8 31 99 5f a8 61 b0 21 a9 65 88 4e 88 48 90 51 89 4b 98 11 d8 0f 10 90 31 8b 75 d8 22 23 | .[.1._.a.!.e.N.H.Q.K......1.u."# |
| 1860 | a0 61 a1 25 90 08 98 15 91 0f d8 10 15 98 11 91 0a 91 05 f0 0d 06 09 1b f4 10 00 12 17 90 75 93 | .a.%..........................u. |
| 1880 | 1c f2 00 02 09 3a 88 41 d8 13 1b 98 41 91 3b 88 44 d8 20 28 a8 14 a1 0e b0 11 d1 20 32 b0 41 b8 | .....:.A....A.;.D..(........2.A. |
| 18a0 | 01 b1 45 d0 0c 1d 88 48 90 54 89 4e 99 41 f0 05 02 09 3a f0 2d 00 0b 0c 88 61 8b 25 f0 32 00 0c | ..E....H.T.N.A....:.-....a.%.2.. |
| 18c0 | 10 f8 f4 43 01 00 0c 0e d7 0b 20 d1 0b 20 f2 00 01 05 15 d9 0f 14 f0 03 01 05 15 fa 73 11 00 00 | ...C........................s... |
| 18e0 | 00 82 11 43 2c 00 c3 2c 13 44 02 03 c4 01 01 44 02 03 63 01 00 00 00 00 00 00 00 00 00 00 00 07 | ...C,..,.D.....D..c............. |
| 1900 | 00 00 00 03 00 00 00 f3 ba 01 00 00 97 00 09 00 74 01 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 | ................t.........|..... |
| 1920 | 00 00 00 00 5c 05 00 00 7d 01 7d 02 7d 03 7d 04 7d 05 7c 04 64 02 6b 28 00 00 73 1a 64 03 7c 02 | ....\...}.}.}.}.}.|.d.k(..s.d.|. |
| 1940 | 7a 05 00 00 7c 04 7a 05 00 00 7c 01 7c 02 7a 00 00 00 64 04 7a 00 00 00 7c 01 7c 02 7a 00 00 00 | z...|.z...|.|.z...d.z...|.|.z... |
| 1960 | 64 04 7a 00 00 00 7a 05 00 00 6b 5c 00 00 72 01 79 05 64 06 5c 04 00 00 7d 06 7d 07 7d 08 7d 09 | d.z...z...k\..r.y.d.\...}.}.}.}. |
| 1980 | 74 07 00 00 00 00 00 00 00 00 7c 01 7c 02 64 04 7a 0a 00 00 64 07 ab 03 00 00 00 00 00 00 44 00 | t.........|.|.d.z...d.........D. |
| 19a0 | 5d 76 00 00 7d 0a 7c 0a 7c 06 64 04 7a 00 00 00 6b 02 00 00 72 02 01 00 79 05 7c 05 7c 0a 19 00 | ]v..}.|.|.d.z...k...r...y.|.|... |
| 19c0 | 00 00 64 02 6b 44 00 00 73 01 8c 16 7c 05 7c 0a 19 00 00 00 7d 0b 7c 0a 7c 06 7c 0b 7a 00 00 00 | ..d.kD..s...|.|.....}.|.|.|.z... |
| 19e0 | 6b 02 00 00 72 05 7c 0a 7c 06 7a 0a 00 00 7d 0b 7c 07 7c 0b 7c 0a 7a 05 00 00 7a 0d 00 00 7d 07 | k...r.|.|.z...}.|.|.|.z...z...}. |
| 1a00 | 74 07 00 00 00 00 00 00 00 00 7c 0b ab 01 00 00 00 00 00 00 44 00 5d 1e 00 00 7d 0c 7c 08 7c 05 | t.........|.........D.]...}.|.|. |
| 1a20 | 7c 06 7c 0c 7a 00 00 00 19 00 00 00 7a 0d 00 00 7d 08 7c 09 7c 06 7c 0c 7a 00 00 00 7c 05 7c 06 | |.|.z.......z...}.|.|.|.z...|.|. |
| 1a40 | 7c 0c 7a 00 00 00 19 00 00 00 7a 05 00 00 7a 0d 00 00 7d 09 8c 20 04 00 7c 06 7c 0b 7a 0d 00 00 | |.z.......z...z...}.....|.|.z... |
| 1a60 | 7d 06 7c 07 7c 06 7c 04 64 04 7a 0a 00 00 7a 05 00 00 7c 06 7c 08 7a 05 00 00 7a 0a 00 00 7c 09 | }.|.|.|.d.z...z...|.|.z...z...|. |
| 1a80 | 7a 00 00 00 6b 44 00 00 73 01 8c 76 01 00 79 01 04 00 79 05 23 00 74 02 00 00 00 00 00 00 00 00 | z...kD..s..v..y...y.#.t......... |
| 1aa0 | 6a 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 24 00 72 03 01 00 59 00 79 01 77 00 | j...................$.r...Y.y.w. |
| 1ac0 | 78 03 59 00 77 01 29 08 75 ef 07 00 00 52 65 74 75 72 6e 73 20 54 72 75 65 20 69 66 20 64 65 67 | x.Y.w.).u....Returns.True.if.deg |
| 1ae0 | 5f 73 65 71 75 65 6e 63 65 20 63 61 6e 20 62 65 20 72 65 61 6c 69 7a 65 64 20 62 79 20 61 20 73 | _sequence.can.be.realized.by.a.s |
| 1b00 | 69 6d 70 6c 65 20 67 72 61 70 68 2e 0a 0a 20 20 20 20 54 68 65 20 76 61 6c 69 64 61 74 69 6f 6e | imple.graph.......The.validation |
| 1b20 | 20 69 73 20 64 6f 6e 65 20 75 73 69 6e 67 20 74 68 65 20 45 72 64 c5 91 73 2d 47 61 6c 6c 61 69 | .is.done.using.the.Erd..s-Gallai |
| 1b40 | 20 74 68 65 6f 72 65 6d 20 5b 45 47 31 39 36 30 5d 5f 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 | .theorem.[EG1960]_.......Paramet |
| 1b60 | 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 64 65 67 5f 73 65 71 75 65 | ers.....----------.....deg_seque |
| 1b80 | 6e 63 65 20 3a 20 6c 69 73 74 0a 20 20 20 20 20 20 20 20 41 20 6c 69 73 74 20 6f 66 20 69 6e 74 | nce.:.list.........A.list.of.int |
| 1ba0 | 65 67 65 72 73 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 | egers......Returns.....-------.. |
| 1bc0 | 20 20 20 76 61 6c 69 64 20 3a 20 62 6f 6f 6c 0a 20 20 20 20 20 20 20 20 54 72 75 65 20 69 66 20 | ...valid.:.bool.........True.if. |
| 1be0 | 64 65 67 5f 73 65 71 75 65 6e 63 65 20 69 73 20 67 72 61 70 68 69 63 61 6c 20 61 6e 64 20 46 61 | deg_sequence.is.graphical.and.Fa |
| 1c00 | 6c 73 65 20 69 66 20 6e 6f 74 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d | lse.if.not.......Examples.....-- |
| 1c20 | 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 47 72 61 70 68 28 5b 28 31 2c | ------.....>>>.G.=.nx.Graph([(1, |
| 1c40 | 20 32 29 2c 20 28 31 2c 20 33 29 2c 20 28 32 2c 20 33 29 2c 20 28 33 2c 20 34 29 2c 20 28 34 2c | .2),.(1,.3),.(2,.3),.(3,.4),.(4, |
| 1c60 | 20 32 29 2c 20 28 35 2c 20 31 29 2c 20 28 35 2c 20 34 29 5d 29 0a 20 20 20 20 3e 3e 3e 20 73 65 | .2),.(5,.1),.(5,.4)]).....>>>.se |
| 1c80 | 71 75 65 6e 63 65 20 3d 20 28 64 20 66 6f 72 20 5f 2c 20 64 20 69 6e 20 47 2e 64 65 67 72 65 65 | quence.=.(d.for._,.d.in.G.degree |
| 1ca0 | 28 29 29 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 69 73 5f 76 61 6c 69 64 5f 64 65 67 72 65 65 5f 73 | ()).....>>>.nx.is_valid_degree_s |
| 1cc0 | 65 71 75 65 6e 63 65 5f 65 72 64 6f 73 5f 67 61 6c 6c 61 69 28 73 65 71 75 65 6e 63 65 29 0a 20 | equence_erdos_gallai(sequence).. |
| 1ce0 | 20 20 20 54 72 75 65 0a 0a 20 20 20 20 54 6f 20 74 65 73 74 20 61 20 6e 6f 6e 2d 76 61 6c 69 64 | ...True......To.test.a.non-valid |
| 1d00 | 20 73 65 71 75 65 6e 63 65 3a 0a 20 20 20 20 3e 3e 3e 20 73 65 71 75 65 6e 63 65 5f 6c 69 73 74 | .sequence:.....>>>.sequence_list |
| 1d20 | 20 3d 20 5b 64 20 66 6f 72 20 5f 2c 20 64 20 69 6e 20 47 2e 64 65 67 72 65 65 28 29 5d 0a 20 20 | .=.[d.for._,.d.in.G.degree()]... |
| 1d40 | 20 20 3e 3e 3e 20 73 65 71 75 65 6e 63 65 5f 6c 69 73 74 5b 2d 31 5d 20 2b 3d 20 31 0a 20 20 20 | ..>>>.sequence_list[-1].+=.1.... |
| 1d60 | 20 3e 3e 3e 20 6e 78 2e 69 73 5f 76 61 6c 69 64 5f 64 65 67 72 65 65 5f 73 65 71 75 65 6e 63 65 | .>>>.nx.is_valid_degree_sequence |
| 1d80 | 5f 65 72 64 6f 73 5f 67 61 6c 6c 61 69 28 73 65 71 75 65 6e 63 65 5f 6c 69 73 74 29 0a 20 20 20 | _erdos_gallai(sequence_list).... |
| 1da0 | 20 46 61 6c 73 65 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a 0a 20 20 20 | .False......Notes.....-----..... |
| 1dc0 | 20 54 68 69 73 20 69 6d 70 6c 65 6d 65 6e 74 61 74 69 6f 6e 20 75 73 65 73 20 61 6e 20 65 71 75 | .This.implementation.uses.an.equ |
| 1de0 | 69 76 61 6c 65 6e 74 20 66 6f 72 6d 20 6f 66 20 74 68 65 20 45 72 64 c5 91 73 2d 47 61 6c 6c 61 | ivalent.form.of.the.Erd..s-Galla |
| 1e00 | 69 20 63 72 69 74 65 72 69 6f 6e 2e 0a 20 20 20 20 57 6f 72 73 74 2d 63 61 73 65 20 72 75 6e 20 | i.criterion......Worst-case.run. |
| 1e20 | 74 69 6d 65 20 69 73 20 24 4f 28 6e 29 24 20 77 68 65 72 65 20 24 6e 24 20 69 73 20 74 68 65 20 | time.is.$O(n)$.where.$n$.is.the. |
| 1e40 | 6c 65 6e 67 74 68 20 6f 66 20 74 68 65 20 73 65 71 75 65 6e 63 65 2e 0a 0a 20 20 20 20 53 70 65 | length.of.the.sequence.......Spe |
| 1e60 | 63 69 66 69 63 61 6c 6c 79 2c 20 61 20 73 65 71 75 65 6e 63 65 20 64 20 69 73 20 67 72 61 70 68 | cifically,.a.sequence.d.is.graph |
| 1e80 | 69 63 61 6c 20 69 66 20 61 6e 64 20 6f 6e 6c 79 20 69 66 20 74 68 65 0a 20 20 20 20 73 75 6d 20 | ical.if.and.only.if.the.....sum. |
| 1ea0 | 6f 66 20 74 68 65 20 73 65 71 75 65 6e 63 65 20 69 73 20 65 76 65 6e 20 61 6e 64 20 66 6f 72 20 | of.the.sequence.is.even.and.for. |
| 1ec0 | 61 6c 6c 20 73 74 72 6f 6e 67 20 69 6e 64 69 63 65 73 20 6b 20 69 6e 20 74 68 65 20 73 65 71 75 | all.strong.indices.k.in.the.sequ |
| 1ee0 | 65 6e 63 65 2c 0a 0a 20 20 20 20 20 2e 2e 20 6d 61 74 68 3a 3a 0a 0a 20 20 20 20 20 20 20 5c 73 | ence,..........math::.........\s |
| 1f00 | 75 6d 5f 7b 69 3d 31 7d 5e 7b 6b 7d 20 64 5f 69 20 5c 6c 65 71 20 6b 28 6b 2d 31 29 20 2b 20 5c | um_{i=1}^{k}.d_i.\leq.k(k-1).+.\ |
| 1f20 | 73 75 6d 5f 7b 6a 3d 6b 2b 31 7d 5e 7b 6e 7d 20 5c 6d 69 6e 28 64 5f 69 2c 6b 29 0a 20 20 20 20 | sum_{j=k+1}^{n}.\min(d_i,k)..... |
| 1f40 | 20 20 20 20 20 20 20 20 20 3d 20 6b 28 6e 2d 31 29 20 2d 20 28 20 6b 20 5c 73 75 6d 5f 7b 6a 3d | .........=.k(n-1).-.(.k.\sum_{j= |
| 1f60 | 30 7d 5e 7b 6b 2d 31 7d 20 6e 5f 6a 20 2d 20 5c 73 75 6d 5f 7b 6a 3d 30 7d 5e 7b 6b 2d 31 7d 20 | 0}^{k-1}.n_j.-.\sum_{j=0}^{k-1}. |
| 1f80 | 6a 20 6e 5f 6a 20 29 0a 0a 20 20 20 20 41 20 73 74 72 6f 6e 67 20 69 6e 64 65 78 20 6b 20 69 73 | j.n_j.)......A.strong.index.k.is |
| 1fa0 | 20 61 6e 79 20 69 6e 64 65 78 20 77 68 65 72 65 20 64 5f 6b 20 3e 3d 20 6b 20 61 6e 64 20 74 68 | .any.index.where.d_k.>=.k.and.th |
| 1fc0 | 65 20 76 61 6c 75 65 20 6e 5f 6a 20 69 73 20 74 68 65 0a 20 20 20 20 6e 75 6d 62 65 72 20 6f 66 | e.value.n_j.is.the.....number.of |
| 1fe0 | 20 6f 63 63 75 72 72 65 6e 63 65 73 20 6f 66 20 6a 20 69 6e 20 64 2e 20 20 54 68 65 20 6d 61 78 | .occurrences.of.j.in.d...The.max |
| 2000 | 69 6d 61 6c 20 73 74 72 6f 6e 67 20 69 6e 64 65 78 20 69 73 20 63 61 6c 6c 65 64 20 74 68 65 0a | imal.strong.index.is.called.the. |
| 2020 | 20 20 20 20 44 75 72 66 65 65 20 69 6e 64 65 78 2e 0a 0a 20 20 20 20 54 68 69 73 20 70 61 72 74 | ....Durfee.index.......This.part |
| 2040 | 69 63 75 6c 61 72 20 72 65 61 72 72 61 6e 67 65 6d 65 6e 74 20 63 6f 6d 65 73 20 66 72 6f 6d 20 | icular.rearrangement.comes.from. |
| 2060 | 74 68 65 20 70 72 6f 6f 66 20 6f 66 20 54 68 65 6f 72 65 6d 20 33 20 69 6e 20 5b 32 5d 5f 2e 0a | the.proof.of.Theorem.3.in.[2]_.. |
| 2080 | 0a 20 20 20 20 54 68 65 20 5a 5a 20 63 6f 6e 64 69 74 69 6f 6e 20 73 61 79 73 20 74 68 61 74 20 | .....The.ZZ.condition.says.that. |
| 20a0 | 66 6f 72 20 74 68 65 20 73 65 71 75 65 6e 63 65 20 64 20 69 66 0a 0a 20 20 20 20 2e 2e 20 6d 61 | for.the.sequence.d.if.........ma |
| 20c0 | 74 68 3a 3a 0a 20 20 20 20 20 20 20 20 7c 64 7c 20 3e 3d 20 5c 66 72 61 63 7b 28 5c 6d 61 78 28 | th::.........|d|.>=.\frac{(\max( |
| 20e0 | 64 29 20 2b 20 5c 6d 69 6e 28 64 29 20 2b 20 31 29 5e 32 7d 7b 34 2a 5c 6d 69 6e 28 64 29 7d 0a | d).+.\min(d).+.1)^2}{4*\min(d)}. |
| 2100 | 0a 20 20 20 20 74 68 65 6e 20 64 20 69 73 20 67 72 61 70 68 69 63 61 6c 2e 20 20 54 68 69 73 20 | .....then.d.is.graphical...This. |
| 2120 | 77 61 73 20 73 68 6f 77 6e 20 69 6e 20 54 68 65 6f 72 65 6d 20 36 20 69 6e 20 5b 32 5d 5f 2e 0a | was.shown.in.Theorem.6.in.[2]_.. |
| 2140 | 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.....----------.. |
| 2160 | 20 20 20 2e 2e 20 5b 31 5d 20 41 2e 20 54 72 69 70 61 74 68 69 20 61 6e 64 20 53 2e 20 56 69 6a | ......[1].A..Tripathi.and.S..Vij |
| 2180 | 61 79 2e 20 22 41 20 6e 6f 74 65 20 6f 6e 20 61 20 74 68 65 6f 72 65 6d 20 6f 66 20 45 72 64 c5 | ay.."A.note.on.a.theorem.of.Erd. |
| 21a0 | 91 73 20 26 20 47 61 6c 6c 61 69 22 2c 0a 20 20 20 20 20 20 20 44 69 73 63 72 65 74 65 20 4d 61 | .s.&.Gallai",........Discrete.Ma |
| 21c0 | 74 68 65 6d 61 74 69 63 73 2c 20 32 36 35 2c 20 70 70 2e 20 34 31 37 2d 34 32 30 20 28 32 30 30 | thematics,.265,.pp..417-420.(200 |
| 21e0 | 33 29 2e 0a 20 20 20 20 2e 2e 20 5b 32 5d 20 49 2e 45 2e 20 5a 76 65 72 6f 76 69 63 68 20 61 6e | 3).........[2].I.E..Zverovich.an |
| 2200 | 64 20 56 2e 45 2e 20 5a 76 65 72 6f 76 69 63 68 2e 20 22 43 6f 6e 74 72 69 62 75 74 69 6f 6e 73 | d.V.E..Zverovich.."Contributions |
| 2220 | 20 74 6f 20 74 68 65 20 74 68 65 6f 72 79 0a 20 20 20 20 20 20 20 6f 66 20 67 72 61 70 68 69 63 | .to.the.theory........of.graphic |
| 2240 | 20 73 65 71 75 65 6e 63 65 73 22 2c 20 44 69 73 63 72 65 74 65 20 4d 61 74 68 65 6d 61 74 69 63 | .sequences",.Discrete.Mathematic |
| 2260 | 73 2c 20 31 30 35 2c 20 70 70 2e 20 32 39 32 2d 33 30 33 20 28 31 39 39 32 29 2e 0a 20 20 20 20 | s,.105,.pp..292-303.(1992)...... |
| 2280 | 2e 2e 20 5b 45 47 31 39 36 30 5d 20 45 72 64 c5 91 73 20 61 6e 64 20 47 61 6c 6c 61 69 2c 20 4d | ...[EG1960].Erd..s.and.Gallai,.M |
| 22a0 | 61 74 2e 20 4c 61 70 6f 6b 20 31 31 20 32 36 34 2c 20 31 39 36 30 2e 0a 20 20 20 20 46 72 02 00 | at..Lapok.11.264,.1960......Fr.. |
| 22c0 | 00 00 72 29 00 00 00 72 17 00 00 00 54 29 04 72 02 00 00 00 72 02 00 00 00 72 02 00 00 00 72 02 | ..r)...r....T).r....r....r....r. |
| 22e0 | 00 00 00 e9 ff ff ff ff 72 2a 00 00 00 29 0d 72 1f 00 00 00 72 22 00 00 00 72 23 00 00 00 72 24 | ........r*...).r....r"...r#...r$ |
| 2300 | 00 00 00 72 25 00 00 00 72 21 00 00 00 72 2e 00 00 00 da 07 73 75 6d 5f 64 65 67 da 06 73 75 6d | ...r%...r!...r......sum_deg..sum |
| 2320 | 5f 6e 6a da 07 73 75 6d 5f 6a 6e 6a da 02 64 6b da 08 72 75 6e 5f 73 69 7a 65 da 01 76 73 0d 00 | _nj..sum_jnj..dk..run_size..vs.. |
| 2340 | 00 00 20 20 20 20 20 20 20 20 20 20 20 20 20 72 14 00 00 00 72 07 00 00 00 72 07 00 00 00 ba 00 | ...............r....r....r...... |
| 2360 | 00 00 73 4a 01 00 00 80 00 f0 40 02 03 05 15 dc 28 3e b8 7c d3 28 4c d1 08 25 88 04 88 64 90 44 | ..sJ......@.....(>.|.(L..%...d.D |
| 2380 | 98 21 98 58 f0 08 00 08 09 88 41 82 76 90 11 90 54 91 18 98 41 91 1c a0 24 a8 14 a1 2b b0 01 a1 | .!.X......A.v...T...A...$...+... |
| 23a0 | 2f b0 64 b8 54 b1 6b c0 41 b1 6f d1 21 46 d2 11 46 d8 0f 13 f0 06 00 23 2d d1 04 1f 80 41 80 77 | /.d.T.k.A.o.!F..F......#-....A.w |
| 23c0 | 90 06 98 07 dc 0e 13 90 44 98 24 a0 11 99 28 a0 42 d3 0e 27 f2 00 0d 05 1d 88 02 d8 0b 0d 90 01 | ........D.$...(.B..'............ |
| 23e0 | 90 41 91 05 8a 3a d9 13 17 d8 0b 13 90 42 89 3c 98 21 d3 0b 1b d8 17 1f a0 02 91 7c 88 48 d8 0f | .A...:.......B.<.!.........|.H.. |
| 2400 | 11 90 41 98 08 91 4c d2 0f 20 d8 1b 1d a0 01 99 36 90 08 d8 0c 13 90 78 a0 22 91 7d d1 0c 24 88 | ..A...L.........6......x.".}..$. |
| 2420 | 47 dc 15 1a 98 38 93 5f f2 00 02 0d 35 90 01 d8 10 16 98 28 a0 31 a0 71 a1 35 99 2f d1 10 29 90 | G....8._....5......(.1.q.5./..). |
| 2440 | 06 d8 10 17 98 41 a0 01 99 45 a0 58 a8 61 b0 21 a9 65 a1 5f d1 1b 34 d1 10 34 91 07 f0 05 02 0d | .....A...E.X.a.!.e._..4..4...... |
| 2460 | 35 f0 06 00 0d 0e 90 18 89 4d 88 41 d8 0f 16 98 11 98 61 a0 21 99 65 99 1b a0 71 a8 36 a1 7a d1 | 5........M.A......a.!.e...q.6.z. |
| 2480 | 19 31 b0 47 d1 19 3b d3 0f 3b d9 17 1c f0 1b 0d 05 1d f0 1c 00 0c 10 f8 f4 2d 00 0c 0e d7 0b 20 | .1.G..;..;...............-...... |
| 24a0 | d1 0b 20 f2 00 01 05 15 d9 0f 14 f0 03 01 05 15 fa 73 11 00 00 00 82 11 43 04 00 c3 04 13 43 1a | .................s......C.....C. |
| 24c0 | 03 c3 19 01 43 1a 03 63 01 00 00 00 00 00 00 00 00 00 00 00 06 00 00 00 03 00 00 00 f3 da 00 00 | ....C..c........................ |
| 24e0 | 00 97 00 09 00 74 00 00 00 00 00 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | .....t.........j................ |
| 2500 | 00 00 00 6a 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 | ...j...................|........ |
| 2520 | 00 7d 01 64 02 5c 02 00 00 7d 02 7d 03 7c 01 44 00 5d 1a 00 00 7d 04 7c 04 64 03 6b 02 00 00 72 | .}.d.\...}.}.|.D.]...}.|.d.k...r |
| 2540 | 02 01 00 79 01 7c 02 7c 04 7a 00 00 00 74 09 00 00 00 00 00 00 00 00 7c 03 7c 04 ab 02 00 00 00 | ...y.|.|.z...t.........|.|...... |
| 2560 | 00 00 00 7d 03 7d 02 8c 1c 04 00 7c 02 64 04 7a 06 00 00 73 08 7c 02 64 04 7c 03 7a 05 00 00 6b | ...}.}.....|.d.z...s.|.d.|.z...k |
| 2580 | 02 00 00 72 01 79 01 79 05 23 00 74 00 00 00 00 00 00 00 00 00 6a 06 00 00 00 00 00 00 00 00 00 | ...r.y.y.#.t.........j.......... |
| 25a0 | 00 00 00 00 00 00 00 00 00 24 00 72 03 01 00 59 00 79 01 77 00 78 03 59 00 77 01 29 06 61 ad 03 | .........$.r...Y.y.w.x.Y.w.).a.. |
| 25c0 | 00 00 52 65 74 75 72 6e 73 20 54 72 75 65 20 69 66 20 73 6f 6d 65 20 6d 75 6c 74 69 67 72 61 70 | ..Returns.True.if.some.multigrap |
| 25e0 | 68 20 63 61 6e 20 72 65 61 6c 69 7a 65 20 74 68 65 20 73 65 71 75 65 6e 63 65 2e 0a 0a 20 20 20 | h.can.realize.the.sequence...... |
| 2600 | 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 73 | .Parameters.....----------.....s |
| 2620 | 65 71 75 65 6e 63 65 20 3a 20 6c 69 73 74 0a 20 20 20 20 20 20 20 20 41 20 6c 69 73 74 20 6f 66 | equence.:.list.........A.list.of |
| 2640 | 20 69 6e 74 65 67 65 72 73 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 2d 2d 2d 2d 2d | .integers......Returns.....----- |
| 2660 | 2d 2d 0a 20 20 20 20 76 61 6c 69 64 20 3a 20 62 6f 6f 6c 0a 20 20 20 20 20 20 20 20 54 72 75 65 | --.....valid.:.bool.........True |
| 2680 | 20 69 66 20 64 65 67 5f 73 65 71 75 65 6e 63 65 20 69 73 20 61 20 6d 75 6c 74 69 67 72 61 70 68 | .if.deg_sequence.is.a.multigraph |
| 26a0 | 69 63 20 64 65 67 72 65 65 20 73 65 71 75 65 6e 63 65 20 61 6e 64 20 46 61 6c 73 65 20 69 66 20 | ic.degree.sequence.and.False.if. |
| 26c0 | 6e 6f 74 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 | not.......Examples.....--------. |
| 26e0 | 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 4d 75 6c 74 69 47 72 61 70 68 28 5b 28 31 2c 20 32 | ....>>>.G.=.nx.MultiGraph([(1,.2 |
| 2700 | 29 2c 20 28 31 2c 20 33 29 2c 20 28 32 2c 20 33 29 2c 20 28 33 2c 20 34 29 2c 20 28 34 2c 20 32 | ),.(1,.3),.(2,.3),.(3,.4),.(4,.2 |
| 2720 | 29 2c 20 28 35 2c 20 31 29 2c 20 28 35 2c 20 34 29 5d 29 0a 20 20 20 20 3e 3e 3e 20 73 65 71 75 | ),.(5,.1),.(5,.4)]).....>>>.sequ |
| 2740 | 65 6e 63 65 20 3d 20 28 64 20 66 6f 72 20 5f 2c 20 64 20 69 6e 20 47 2e 64 65 67 72 65 65 28 29 | ence.=.(d.for._,.d.in.G.degree() |
| 2760 | 29 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 69 73 5f 6d 75 6c 74 69 67 72 61 70 68 69 63 61 6c 28 73 | ).....>>>.nx.is_multigraphical(s |
| 2780 | 65 71 75 65 6e 63 65 29 0a 20 20 20 20 54 72 75 65 0a 0a 20 20 20 20 54 6f 20 74 65 73 74 20 61 | equence).....True......To.test.a |
| 27a0 | 20 6e 6f 6e 2d 6d 75 6c 74 69 67 72 61 70 68 69 63 61 6c 20 73 65 71 75 65 6e 63 65 3a 0a 20 20 | .non-multigraphical.sequence:... |
| 27c0 | 20 20 3e 3e 3e 20 73 65 71 75 65 6e 63 65 5f 6c 69 73 74 20 3d 20 5b 64 20 66 6f 72 20 5f 2c 20 | ..>>>.sequence_list.=.[d.for._,. |
| 27e0 | 64 20 69 6e 20 47 2e 64 65 67 72 65 65 28 29 5d 0a 20 20 20 20 3e 3e 3e 20 73 65 71 75 65 6e 63 | d.in.G.degree()].....>>>.sequenc |
| 2800 | 65 5f 6c 69 73 74 5b 2d 31 5d 20 2b 3d 20 31 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 69 73 5f 6d 75 | e_list[-1].+=.1.....>>>.nx.is_mu |
| 2820 | 6c 74 69 67 72 61 70 68 69 63 61 6c 28 73 65 71 75 65 6e 63 65 5f 6c 69 73 74 29 0a 20 20 20 20 | ltigraphical(sequence_list)..... |
| 2840 | 46 61 6c 73 65 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 | False......Notes.....-----.....T |
| 2860 | 68 65 20 77 6f 72 73 74 2d 63 61 73 65 20 72 75 6e 20 74 69 6d 65 20 69 73 20 24 4f 28 6e 29 24 | he.worst-case.run.time.is.$O(n)$ |
| 2880 | 20 77 68 65 72 65 20 24 6e 24 20 69 73 20 74 68 65 20 6c 65 6e 67 74 68 20 6f 66 20 74 68 65 20 | .where.$n$.is.the.length.of.the. |
| 28a0 | 73 65 71 75 65 6e 63 65 2e 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d | sequence.......References.....-- |
| 28c0 | 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 53 2e 20 4c 2e 20 48 61 6b 69 6d 69 | --------........[1].S..L..Hakimi |
| 28e0 | 2e 20 22 4f 6e 20 74 68 65 20 72 65 61 6c 69 7a 61 62 69 6c 69 74 79 20 6f 66 20 61 20 73 65 74 | .."On.the.realizability.of.a.set |
| 2900 | 20 6f 66 20 69 6e 74 65 67 65 72 73 20 61 73 0a 20 20 20 20 20 20 20 64 65 67 72 65 65 73 20 6f | .of.integers.as........degrees.o |
| 2920 | 66 20 74 68 65 20 76 65 72 74 69 63 65 73 20 6f 66 20 61 20 6c 69 6e 65 61 72 20 67 72 61 70 68 | f.the.vertices.of.a.linear.graph |
| 2940 | 22 2c 20 4a 2e 20 53 49 41 4d 2c 20 31 30 2c 20 70 70 2e 20 34 39 36 2d 35 30 36 0a 20 20 20 20 | ",.J..SIAM,.10,.pp..496-506..... |
| 2960 | 20 20 20 28 31 39 36 32 29 2e 0a 20 20 20 20 46 a9 02 72 02 00 00 00 72 02 00 00 00 72 02 00 00 | ...(1962)......F..r....r....r... |
| 2980 | 00 72 18 00 00 00 54 29 05 72 0e 00 00 00 72 19 00 00 00 72 1a 00 00 00 da 0d 4e 65 74 77 6f 72 | .r....T).r....r....r......Networ |
| 29a0 | 6b 58 45 72 72 6f 72 72 1d 00 00 00 29 05 72 10 00 00 00 72 1f 00 00 00 72 24 00 00 00 72 22 00 | kXErrorr....).r....r....r$...r". |
| 29c0 | 00 00 72 26 00 00 00 73 05 00 00 00 20 20 20 20 20 72 14 00 00 00 72 04 00 00 00 72 04 00 00 00 | ..r&...s.........r....r....r.... |
| 29e0 | 15 01 00 00 73 86 00 00 00 80 00 f0 4a 01 03 05 15 dc 17 19 97 78 91 78 d7 17 31 d1 17 31 b0 28 | ....s.......J........x.x..1..1.( |
| 2a00 | d3 17 3b 88 0c f0 06 00 12 16 81 4a 80 44 88 24 d8 0d 19 f2 00 03 05 2c 88 01 d8 0b 0c 88 71 8a | ..;........J.D.$.......,......q. |
| 2a20 | 35 d9 13 18 d8 15 19 98 41 91 58 9c 73 a0 34 a8 11 9b 7c 88 64 89 04 f0 07 03 05 2c f0 08 00 08 | 5.......A.X.s.4...|.d......,.... |
| 2a40 | 0c 88 61 82 78 90 34 98 21 98 64 99 28 92 3f d8 0f 14 d8 0b 0f f8 f4 13 00 0c 0e d7 0b 1b d1 0b | ..a.x.4.!.d.(.?................. |
| 2a60 | 1b f2 00 01 05 15 d9 0f 14 f0 03 01 05 15 fa 73 11 00 00 00 82 1f 41 14 00 c1 14 13 41 2a 03 c1 | ...............s......A.....A*.. |
| 2a80 | 29 01 41 2a 03 63 01 00 00 00 00 00 00 00 00 00 00 00 04 00 00 00 03 00 00 00 f3 b6 00 00 00 97 | ).A*.c.......................... |
| 2aa0 | 00 09 00 74 00 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 | ...t.........j.................. |
| 2ac0 | 00 6a 05 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 7d | .j...................|.........} |
| 2ae0 | 01 74 09 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 64 02 7a 06 00 00 64 03 6b 28 00 | .t.........|.........d.z...d.k(. |
| 2b00 | 00 78 01 72 0e 01 00 74 0b 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 64 03 6b 5c 00 | .x.r...t.........|.........d.k\. |
| 2b20 | 00 53 00 23 00 74 00 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 | .S.#.t.........j................ |
| 2b40 | 00 00 00 24 00 72 03 01 00 59 00 79 01 77 00 78 03 59 00 77 01 29 04 61 3a 04 00 00 52 65 74 75 | ...$.r...Y.y.w.x.Y.w.).a:...Retu |
| 2b60 | 72 6e 73 20 54 72 75 65 20 69 66 20 73 6f 6d 65 20 70 73 65 75 64 6f 67 72 61 70 68 20 63 61 6e | rns.True.if.some.pseudograph.can |
| 2b80 | 20 72 65 61 6c 69 7a 65 20 74 68 65 20 73 65 71 75 65 6e 63 65 2e 0a 0a 20 20 20 20 45 76 65 72 | .realize.the.sequence.......Ever |
| 2ba0 | 79 20 6e 6f 6e 6e 65 67 61 74 69 76 65 20 69 6e 74 65 67 65 72 20 73 65 71 75 65 6e 63 65 20 77 | y.nonnegative.integer.sequence.w |
| 2bc0 | 69 74 68 20 61 6e 20 65 76 65 6e 20 73 75 6d 20 69 73 20 70 73 65 75 64 6f 67 72 61 70 68 69 63 | ith.an.even.sum.is.pseudographic |
| 2be0 | 61 6c 0a 20 20 20 20 28 73 65 65 20 5b 31 5d 5f 29 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 | al.....(see.[1]_).......Paramete |
| 2c00 | 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 73 65 71 75 65 6e 63 65 20 3a | rs.....----------.....sequence.: |
| 2c20 | 20 6c 69 73 74 20 6f 72 20 69 74 65 72 61 62 6c 65 20 63 6f 6e 74 61 69 6e 65 72 0a 20 20 20 20 | .list.or.iterable.container..... |
| 2c40 | 20 20 20 20 41 20 73 65 71 75 65 6e 63 65 20 6f 66 20 69 6e 74 65 67 65 72 20 6e 6f 64 65 20 64 | ....A.sequence.of.integer.node.d |
| 2c60 | 65 67 72 65 65 73 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 | egrees......Returns.....-------. |
| 2c80 | 20 20 20 20 76 61 6c 69 64 20 3a 20 62 6f 6f 6c 0a 20 20 20 20 20 20 54 72 75 65 20 69 66 20 74 | ....valid.:.bool.......True.if.t |
| 2ca0 | 68 65 20 73 65 71 75 65 6e 63 65 20 69 73 20 61 20 70 73 65 75 64 6f 67 72 61 70 68 69 63 20 64 | he.sequence.is.a.pseudographic.d |
| 2cc0 | 65 67 72 65 65 20 73 65 71 75 65 6e 63 65 20 61 6e 64 20 46 61 6c 73 65 20 69 66 20 6e 6f 74 2e | egree.sequence.and.False.if.not. |
| 2ce0 | 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 20 20 20 20 | ......Examples.....--------..... |
| 2d00 | 3e 3e 3e 20 47 20 3d 20 6e 78 2e 47 72 61 70 68 28 5b 28 31 2c 20 32 29 2c 20 28 31 2c 20 33 29 | >>>.G.=.nx.Graph([(1,.2),.(1,.3) |
| 2d20 | 2c 20 28 32 2c 20 33 29 2c 20 28 33 2c 20 34 29 2c 20 28 34 2c 20 32 29 2c 20 28 35 2c 20 31 29 | ,.(2,.3),.(3,.4),.(4,.2),.(5,.1) |
| 2d40 | 2c 20 28 35 2c 20 34 29 5d 29 0a 20 20 20 20 3e 3e 3e 20 73 65 71 75 65 6e 63 65 20 3d 20 28 64 | ,.(5,.4)]).....>>>.sequence.=.(d |
| 2d60 | 20 66 6f 72 20 5f 2c 20 64 20 69 6e 20 47 2e 64 65 67 72 65 65 28 29 29 0a 20 20 20 20 3e 3e 3e | .for._,.d.in.G.degree()).....>>> |
| 2d80 | 20 6e 78 2e 69 73 5f 70 73 65 75 64 6f 67 72 61 70 68 69 63 61 6c 28 73 65 71 75 65 6e 63 65 29 | .nx.is_pseudographical(sequence) |
| 2da0 | 0a 20 20 20 20 54 72 75 65 0a 0a 20 20 20 20 54 6f 20 74 65 73 74 20 61 20 6e 6f 6e 2d 70 73 65 | .....True......To.test.a.non-pse |
| 2dc0 | 75 64 6f 67 72 61 70 68 69 63 61 6c 20 73 65 71 75 65 6e 63 65 3a 0a 20 20 20 20 3e 3e 3e 20 73 | udographical.sequence:.....>>>.s |
| 2de0 | 65 71 75 65 6e 63 65 5f 6c 69 73 74 20 3d 20 5b 64 20 66 6f 72 20 5f 2c 20 64 20 69 6e 20 47 2e | equence_list.=.[d.for._,.d.in.G. |
| 2e00 | 64 65 67 72 65 65 28 29 5d 0a 20 20 20 20 3e 3e 3e 20 73 65 71 75 65 6e 63 65 5f 6c 69 73 74 5b | degree()].....>>>.sequence_list[ |
| 2e20 | 2d 31 5d 20 2b 3d 20 31 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 69 73 5f 70 73 65 75 64 6f 67 72 61 | -1].+=.1.....>>>.nx.is_pseudogra |
| 2e40 | 70 68 69 63 61 6c 28 73 65 71 75 65 6e 63 65 5f 6c 69 73 74 29 0a 20 20 20 20 46 61 6c 73 65 0a | phical(sequence_list).....False. |
| 2e60 | 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 65 20 77 6f 72 | .....Notes.....-----.....The.wor |
| 2e80 | 73 74 2d 63 61 73 65 20 72 75 6e 20 74 69 6d 65 20 69 73 20 24 4f 28 6e 29 24 20 77 68 65 72 65 | st-case.run.time.is.$O(n)$.where |
| 2ea0 | 20 6e 20 69 73 20 74 68 65 20 6c 65 6e 67 74 68 20 6f 66 20 74 68 65 20 73 65 71 75 65 6e 63 65 | .n.is.the.length.of.the.sequence |
| 2ec0 | 2e 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d | .......References.....---------- |
| 2ee0 | 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 46 2e 20 42 6f 65 73 63 68 20 61 6e 64 20 46 2e 20 48 61 72 | ........[1].F..Boesch.and.F..Har |
| 2f00 | 61 72 79 2e 20 22 4c 69 6e 65 20 72 65 6d 6f 76 61 6c 20 61 6c 67 6f 72 69 74 68 6d 73 20 66 6f | ary.."Line.removal.algorithms.fo |
| 2f20 | 72 20 67 72 61 70 68 73 0a 20 20 20 20 20 20 20 61 6e 64 20 74 68 65 69 72 20 64 65 67 72 65 65 | r.graphs........and.their.degree |
| 2f40 | 20 6c 69 73 74 73 22 2c 20 49 45 45 45 20 54 72 61 6e 73 2e 20 43 69 72 63 75 69 74 73 20 61 6e | .lists",.IEEE.Trans..Circuits.an |
| 2f60 | 64 20 53 79 73 74 65 6d 73 2c 20 43 41 53 2d 32 33 28 31 32 29 2c 0a 20 20 20 20 20 20 20 70 70 | d.Systems,.CAS-23(12),........pp |
| 2f80 | 2e 20 37 37 38 2d 37 38 32 20 28 31 39 37 36 29 2e 0a 20 20 20 20 46 72 18 00 00 00 72 02 00 00 | ..778-782.(1976)......Fr....r... |
| 2fa0 | 00 29 06 72 0e 00 00 00 72 19 00 00 00 72 1a 00 00 00 72 3b 00 00 00 da 03 73 75 6d 72 1e 00 00 | .).r....r....r....r;.....sumr... |
| 2fc0 | 00 29 02 72 10 00 00 00 72 1f 00 00 00 73 02 00 00 00 20 20 72 14 00 00 00 72 05 00 00 00 72 05 | .).r....r....s......r....r....r. |
| 2fe0 | 00 00 00 48 01 00 00 73 5c 00 00 00 80 00 f0 50 01 03 05 15 dc 17 19 97 78 91 78 d7 17 31 d1 17 | ...H...s\......P........x.x..1.. |
| 3000 | 31 b0 28 d3 17 3b 88 0c f4 06 00 0c 0f 88 7c d3 0b 1c 98 71 d1 0b 20 a0 41 d1 0b 25 d2 0b 40 ac | 1.(..;........|....q....A..%..@. |
| 3020 | 23 a8 6c d3 2a 3b b8 71 d1 2a 40 d0 04 40 f8 f4 05 00 0c 0e d7 0b 1b d1 0b 1b f2 00 01 05 15 d9 | #.l.*;.q.*@..@.................. |
| 3040 | 0f 14 f0 03 01 05 15 fa 73 11 00 00 00 82 1f 41 02 00 c1 02 13 41 18 03 c1 17 01 41 18 03 63 02 | ........s......A.....A.....A..c. |
| 3060 | 00 00 00 00 00 00 00 00 00 00 00 07 00 00 00 03 00 00 00 f3 d6 04 00 00 97 00 09 00 74 00 00 00 | ............................t... |
| 3080 | 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 6a 05 00 00 00 00 | ......j...................j..... |
| 30a0 | 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 00 ab 01 00 00 00 00 00 00 7d 02 74 00 00 00 00 00 | ..............|.........}.t..... |
| 30c0 | 00 00 00 00 6a 02 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 6a 05 00 00 00 00 00 00 | ....j...................j....... |
| 30e0 | 00 00 00 00 00 00 00 00 00 00 00 00 7c 01 ab 01 00 00 00 00 00 00 7d 03 64 02 64 02 74 09 00 00 | ............|.........}.d.d.t... |
| 3100 | 00 00 00 00 00 00 7c 02 ab 01 00 00 00 00 00 00 74 09 00 00 00 00 00 00 00 00 7c 03 ab 01 00 00 | ......|.........t.........|..... |
| 3120 | 00 00 00 00 66 04 5c 04 00 00 7d 04 7d 05 7d 06 7d 07 74 0b 00 00 00 00 00 00 00 00 7c 06 7c 07 | ....f.\...}.}.}.}.t.........|.|. |
| 3140 | ab 02 00 00 00 00 00 00 7d 08 64 02 7d 09 7c 08 64 02 6b 28 00 00 72 01 79 03 67 00 67 00 7d 0b | ........}.d.}.|.d.k(..r.y.g.g.}. |
| 3160 | 7d 0a 74 0d 00 00 00 00 00 00 00 00 7c 08 ab 01 00 00 00 00 00 00 44 00 5d 76 00 00 7d 0c 64 04 | }.t.........|.........D.]v..}.d. |
| 3180 | 5c 02 00 00 7d 0d 7d 0e 7c 0c 7c 07 6b 02 00 00 72 05 7c 03 7c 0c 19 00 00 00 7d 0e 7c 0c 7c 06 | \...}.}.|.|.k...r.|.|.....}.|.|. |
| 31a0 | 6b 02 00 00 72 05 7c 02 7c 0c 19 00 00 00 7d 0d 7c 0d 64 02 6b 02 00 00 73 05 7c 0e 64 02 6b 02 | k...r.|.|.....}.|.d.k...s.|.d.k. |
| 31c0 | 00 00 72 02 01 00 79 01 7c 04 7c 0d 7a 00 00 00 7c 05 7c 0e 7a 00 00 00 74 0b 00 00 00 00 00 00 | ..r...y.|.|.z...|.|.z...t....... |
| 31e0 | 00 00 7c 09 7c 0d ab 02 00 00 00 00 00 00 7d 09 7d 05 7d 04 7c 0d 64 02 6b 44 00 00 72 1a 7c 0a | ..|.|.........}.}.}.|.d.kD..r.|. |
| 3200 | 6a 0f 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 05 7c 0e 7a 05 00 00 64 05 7c 0d | j...................d.|.z...d.|. |
| 3220 | 7a 05 00 00 66 02 ab 01 00 00 00 00 00 00 01 00 8c 5d 7c 0e 64 02 6b 44 00 00 73 01 8c 63 7c 0b | z...f............]|.d.kD..s..c|. |
| 3240 | 6a 0f 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 64 05 7c 0e 7a 05 00 00 ab 01 00 00 | j...................d.|.z....... |
| 3260 | 00 00 00 00 01 00 8c 78 04 00 7c 04 7c 05 6b 37 00 00 72 01 79 01 74 11 00 00 00 00 00 00 00 00 | .......x..|.|.k7..r.y.t......... |
| 3280 | 6a 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0a ab 01 00 00 00 00 00 00 01 00 | j...................|........... |
| 32a0 | 74 11 00 00 00 00 00 00 00 00 6a 12 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0b | t.........j...................|. |
| 32c0 | ab 01 00 00 00 00 00 00 01 00 64 04 67 01 7c 09 64 06 7a 00 00 00 7a 05 00 00 7d 0f 7c 0a 90 01 | ..........d.g.|.d.z...z...}.|... |
| 32e0 | 72 1c 74 11 00 00 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 | r.t.........j................... |
| 3300 | 7c 0a ab 01 00 00 00 00 00 00 5c 02 00 00 7d 10 7d 11 7c 11 64 05 7a 12 00 00 7d 11 7c 11 74 09 | |.........\...}.}.|.d.z...}.|.t. |
| 3320 | 00 00 00 00 00 00 00 00 7c 0a ab 01 00 00 00 00 00 00 74 09 00 00 00 00 00 00 00 00 7c 0b ab 01 | ........|.........t.........|... |
| 3340 | 00 00 00 00 00 00 7a 00 00 00 6b 44 00 00 72 01 79 01 64 02 7d 12 74 0d 00 00 00 00 00 00 00 00 | ......z...kD..r.y.d.}.t......... |
| 3360 | 7c 11 ab 01 00 00 00 00 00 00 44 00 5d 68 00 00 7d 13 7c 0b 72 28 7c 0a 72 0e 7c 0a 64 02 19 00 | |.........D.]h..}.|.r(|.r.|.d... |
| 3380 | 00 00 64 02 19 00 00 00 7c 0b 64 02 19 00 00 00 6b 44 00 00 72 18 74 11 00 00 00 00 00 00 00 00 | ..d.....|.d.....kD..r.t......... |
| 33a0 | 6a 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0b ab 01 00 00 00 00 00 00 7d 14 | j...................|.........}. |
| 33c0 | 64 02 7d 15 6e 18 74 11 00 00 00 00 00 00 00 00 6a 14 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | d.}.n.t.........j............... |
| 33e0 | 00 00 00 00 7c 0a ab 01 00 00 00 00 00 00 5c 02 00 00 7d 14 7d 15 7c 14 64 02 6b 28 00 00 72 02 | ....|.........\...}.}.|.d.k(..r. |
| 3400 | 01 00 79 01 7c 14 64 06 7a 00 00 00 64 02 6b 02 00 00 73 06 7c 15 64 02 6b 02 00 00 73 01 8c 5a | ..y.|.d.z...d.k...s.|.d.k...s..Z |
| 3420 | 7c 14 64 06 7a 00 00 00 7c 15 66 02 7c 0f 7c 12 3c 00 00 00 7c 12 64 06 7a 0d 00 00 7d 12 8c 6a | |.d.z...|.f.|.|.<...|.d.z...}..j |
| 3440 | 04 00 74 0d 00 00 00 00 00 00 00 00 7c 12 ab 01 00 00 00 00 00 00 44 00 5d 3f 00 00 7d 13 7c 0f | ..t.........|.........D.]?..}.|. |
| 3460 | 7c 13 19 00 00 00 7d 16 7c 16 64 06 19 00 00 00 64 02 6b 02 00 00 72 17 74 11 00 00 00 00 00 00 | |.....}.|.d.....d.k...r.t....... |
| 3480 | 00 00 6a 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0a 7c 16 ab 02 00 00 00 00 | ..j...................|.|....... |
| 34a0 | 00 00 01 00 8c 27 74 11 00 00 00 00 00 00 00 00 6a 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | .....'t.........j............... |
| 34c0 | 00 00 00 00 7c 0b 7c 16 64 02 19 00 00 00 ab 02 00 00 00 00 00 00 01 00 8c 41 04 00 7c 10 64 02 | ....|.|.d................A..|.d. |
| 34e0 | 6b 02 00 00 72 16 74 11 00 00 00 00 00 00 00 00 6a 16 00 00 00 00 00 00 00 00 00 00 00 00 00 00 | k...r.t.........j............... |
| 3500 | 00 00 00 00 7c 0b 7c 10 ab 02 00 00 00 00 00 00 01 00 7c 0a 72 02 90 01 8c 1c 79 03 23 00 74 00 | ....|.|...........|.r.....y.#.t. |
| 3520 | 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 24 00 72 03 | ........j...................$.r. |
| 3540 | 01 00 59 00 79 01 77 00 78 03 59 00 77 01 29 07 61 e8 04 00 00 52 65 74 75 72 6e 73 20 54 72 75 | ..Y.y.w.x.Y.w.).a....Returns.Tru |
| 3560 | 65 20 69 66 20 73 6f 6d 65 20 64 69 72 65 63 74 65 64 20 67 72 61 70 68 20 63 61 6e 20 72 65 61 | e.if.some.directed.graph.can.rea |
| 3580 | 6c 69 7a 65 20 74 68 65 20 69 6e 2d 20 61 6e 64 20 6f 75 74 2d 64 65 67 72 65 65 0a 20 20 20 20 | lize.the.in-.and.out-degree..... |
| 35a0 | 73 65 71 75 65 6e 63 65 73 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d | sequences.......Parameters.....- |
| 35c0 | 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 69 6e 5f 73 65 71 75 65 6e 63 65 20 3a 20 6c 69 73 74 | ---------.....in_sequence.:.list |
| 35e0 | 20 6f 72 20 69 74 65 72 61 62 6c 65 20 63 6f 6e 74 61 69 6e 65 72 0a 20 20 20 20 20 20 20 20 41 | .or.iterable.container.........A |
| 3600 | 20 73 65 71 75 65 6e 63 65 20 6f 66 20 69 6e 74 65 67 65 72 20 6e 6f 64 65 20 69 6e 2d 64 65 67 | .sequence.of.integer.node.in-deg |
| 3620 | 72 65 65 73 0a 0a 20 20 20 20 6f 75 74 5f 73 65 71 75 65 6e 63 65 20 3a 20 6c 69 73 74 20 6f 72 | rees......out_sequence.:.list.or |
| 3640 | 20 69 74 65 72 61 62 6c 65 20 63 6f 6e 74 61 69 6e 65 72 0a 20 20 20 20 20 20 20 20 41 20 73 65 | .iterable.container.........A.se |
| 3660 | 71 75 65 6e 63 65 20 6f 66 20 69 6e 74 65 67 65 72 20 6e 6f 64 65 20 6f 75 74 2d 64 65 67 72 65 | quence.of.integer.node.out-degre |
| 3680 | 65 73 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 | es......Returns.....-------..... |
| 36a0 | 76 61 6c 69 64 20 3a 20 62 6f 6f 6c 0a 20 20 20 20 20 20 54 72 75 65 20 69 66 20 69 6e 20 61 6e | valid.:.bool.......True.if.in.an |
| 36c0 | 64 20 6f 75 74 2d 73 65 71 75 65 6e 63 65 73 20 61 72 65 20 64 69 67 72 61 70 68 69 63 20 46 61 | d.out-sequences.are.digraphic.Fa |
| 36e0 | 6c 73 65 20 69 66 20 6e 6f 74 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 20 2d 2d | lse.if.not.......Examples.....-- |
| 3700 | 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 47 20 3d 20 6e 78 2e 44 69 47 72 61 70 68 28 5b 28 | ------.....>>>.G.=.nx.DiGraph([( |
| 3720 | 31 2c 20 32 29 2c 20 28 31 2c 20 33 29 2c 20 28 32 2c 20 33 29 2c 20 28 33 2c 20 34 29 2c 20 28 | 1,.2),.(1,.3),.(2,.3),.(3,.4),.( |
| 3740 | 34 2c 20 32 29 2c 20 28 35 2c 20 31 29 2c 20 28 35 2c 20 34 29 5d 29 0a 20 20 20 20 3e 3e 3e 20 | 4,.2),.(5,.1),.(5,.4)]).....>>>. |
| 3760 | 69 6e 5f 73 65 71 20 3d 20 28 64 20 66 6f 72 20 6e 2c 20 64 20 69 6e 20 47 2e 69 6e 5f 64 65 67 | in_seq.=.(d.for.n,.d.in.G.in_deg |
| 3780 | 72 65 65 28 29 29 0a 20 20 20 20 3e 3e 3e 20 6f 75 74 5f 73 65 71 20 3d 20 28 64 20 66 6f 72 20 | ree()).....>>>.out_seq.=.(d.for. |
| 37a0 | 6e 2c 20 64 20 69 6e 20 47 2e 6f 75 74 5f 64 65 67 72 65 65 28 29 29 0a 20 20 20 20 3e 3e 3e 20 | n,.d.in.G.out_degree()).....>>>. |
| 37c0 | 6e 78 2e 69 73 5f 64 69 67 72 61 70 68 69 63 61 6c 28 69 6e 5f 73 65 71 2c 20 6f 75 74 5f 73 65 | nx.is_digraphical(in_seq,.out_se |
| 37e0 | 71 29 0a 20 20 20 20 54 72 75 65 0a 0a 20 20 20 20 54 6f 20 74 65 73 74 20 61 20 6e 6f 6e 2d 64 | q).....True......To.test.a.non-d |
| 3800 | 69 67 72 61 70 68 69 63 61 6c 20 73 63 65 6e 61 72 69 6f 3a 0a 20 20 20 20 3e 3e 3e 20 69 6e 5f | igraphical.scenario:.....>>>.in_ |
| 3820 | 73 65 71 5f 6c 69 73 74 20 3d 20 5b 64 20 66 6f 72 20 6e 2c 20 64 20 69 6e 20 47 2e 69 6e 5f 64 | seq_list.=.[d.for.n,.d.in.G.in_d |
| 3840 | 65 67 72 65 65 28 29 5d 0a 20 20 20 20 3e 3e 3e 20 69 6e 5f 73 65 71 5f 6c 69 73 74 5b 2d 31 5d | egree()].....>>>.in_seq_list[-1] |
| 3860 | 20 2b 3d 20 31 0a 20 20 20 20 3e 3e 3e 20 6e 78 2e 69 73 5f 64 69 67 72 61 70 68 69 63 61 6c 28 | .+=.1.....>>>.nx.is_digraphical( |
| 3880 | 69 6e 5f 73 65 71 5f 6c 69 73 74 2c 20 6f 75 74 5f 73 65 71 29 0a 20 20 20 20 46 61 6c 73 65 0a | in_seq_list,.out_seq).....False. |
| 38a0 | 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 61 6c | .....Notes.....-----.....This.al |
| 38c0 | 67 6f 72 69 74 68 6d 20 69 73 20 66 72 6f 6d 20 4b 6c 65 69 74 6d 61 6e 20 61 6e 64 20 57 61 6e | gorithm.is.from.Kleitman.and.Wan |
| 38e0 | 67 20 5b 31 5d 5f 2e 0a 20 20 20 20 54 68 65 20 77 6f 72 73 74 20 63 61 73 65 20 72 75 6e 74 69 | g.[1]_......The.worst.case.runti |
| 3900 | 6d 65 20 69 73 20 24 4f 28 73 20 5c 74 69 6d 65 73 20 5c 6c 6f 67 20 6e 29 24 20 77 68 65 72 65 | me.is.$O(s.\times.\log.n)$.where |
| 3920 | 20 24 73 24 20 61 6e 64 20 24 6e 24 20 61 72 65 20 74 68 65 0a 20 20 20 20 73 75 6d 20 61 6e 64 | .$s$.and.$n$.are.the.....sum.and |
| 3940 | 20 6c 65 6e 67 74 68 20 6f 66 20 74 68 65 20 73 65 71 75 65 6e 63 65 73 20 72 65 73 70 65 63 74 | .length.of.the.sequences.respect |
| 3960 | 69 76 65 6c 79 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 | ively.......References.....----- |
| 3980 | 2d 2d 2d 2d 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 44 2e 4a 2e 20 4b 6c 65 69 74 6d 61 6e 20 61 | -----........[1].D.J..Kleitman.a |
| 39a0 | 6e 64 20 44 2e 4c 2e 20 57 61 6e 67 0a 20 20 20 20 20 20 20 41 6c 67 6f 72 69 74 68 6d 73 20 66 | nd.D.L..Wang........Algorithms.f |
| 39c0 | 6f 72 20 43 6f 6e 73 74 72 75 63 74 69 6e 67 20 47 72 61 70 68 73 20 61 6e 64 20 44 69 67 72 61 | or.Constructing.Graphs.and.Digra |
| 39e0 | 70 68 73 20 77 69 74 68 20 47 69 76 65 6e 20 56 61 6c 65 6e 63 65 73 0a 20 20 20 20 20 20 20 61 | phs.with.Given.Valences........a |
| 3a00 | 6e 64 20 46 61 63 74 6f 72 73 2c 20 44 69 73 63 72 65 74 65 20 4d 61 74 68 65 6d 61 74 69 63 73 | nd.Factors,.Discrete.Mathematics |
| 3a20 | 2c 20 36 28 31 29 2c 20 70 70 2e 20 37 39 2d 38 38 20 28 31 39 37 33 29 0a 20 20 20 20 46 72 02 | ,.6(1),.pp..79-88.(1973).....Fr. |
| 3a40 | 00 00 00 54 72 3a 00 00 00 72 32 00 00 00 72 17 00 00 00 29 0c 72 0e 00 00 00 72 19 00 00 00 72 | ...Tr:...r2...r....).r....r....r |
| 3a60 | 1a 00 00 00 72 3b 00 00 00 72 1b 00 00 00 72 1d 00 00 00 72 2b 00 00 00 da 06 61 70 70 65 6e 64 | ....r;...r....r....r+.....append |
| 3a80 | da 05 68 65 61 70 71 da 07 68 65 61 70 69 66 79 da 07 68 65 61 70 70 6f 70 da 08 68 65 61 70 70 | ..heapq..heapify..heappop..heapp |
| 3aa0 | 75 73 68 29 17 da 0b 69 6e 5f 73 65 71 75 65 6e 63 65 da 0c 6f 75 74 5f 73 65 71 75 65 6e 63 65 | ush)...in_sequence..out_sequence |
| 3ac0 | da 0f 69 6e 5f 64 65 67 5f 73 65 71 75 65 6e 63 65 da 10 6f 75 74 5f 64 65 67 5f 73 65 71 75 65 | ..in_deg_sequence..out_deg_seque |
| 3ae0 | 6e 63 65 da 05 73 75 6d 69 6e da 06 73 75 6d 6f 75 74 da 03 6e 69 6e da 04 6e 6f 75 74 da 04 6d | nce..sumin..sumout..nin..nout..m |
| 3b00 | 61 78 6e da 05 6d 61 78 69 6e da 08 73 74 75 62 68 65 61 70 da 08 7a 65 72 6f 68 65 61 70 72 25 | axn..maxin..stubheap..zeroheapr% |
| 3b20 | 00 00 00 da 06 69 6e 5f 64 65 67 da 07 6f 75 74 5f 64 65 67 72 2c 00 00 00 da 07 66 72 65 65 6f | .....in_deg..out_degr,.....freeo |
| 3b40 | 75 74 da 06 66 72 65 65 69 6e 72 2d 00 00 00 72 2f 00 00 00 da 07 73 74 75 62 6f 75 74 da 06 73 | ut..freeinr-...r/.....stubout..s |
| 3b60 | 74 75 62 69 6e 72 30 00 00 00 73 17 00 00 00 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | tubinr0...s..................... |
| 3b80 | 20 20 20 20 20 20 72 14 00 00 00 72 06 00 00 00 72 06 00 00 00 77 01 00 00 73 98 02 00 00 80 00 | ......r....r....r....w...s...... |
| 3ba0 | f0 58 01 04 05 15 dc 1a 1c 9f 28 99 28 d7 1a 34 d1 1a 34 b0 5b d3 1a 41 88 0f dc 1b 1d 9f 38 99 | .X........(.(..4..4.[..A......8. |
| 3bc0 | 38 d7 1b 35 d1 1b 35 b0 6c d3 1b 43 d0 08 18 f0 0a 00 20 21 a0 21 a4 53 a8 1f d3 25 39 bc 33 d0 | 8..5..5.l..C.......!.!.S...%9.3. |
| 3be0 | 3f 4f d3 3b 50 d0 1f 50 d1 04 1c 80 45 88 36 90 33 98 04 dc 0b 0e 88 73 90 44 8b 3e 80 44 d8 0c | ?O.;P..P....E.6.3......s.D.>.D.. |
| 3c00 | 0d 80 45 d8 07 0b 88 71 82 79 d8 0f 13 d8 19 1b 98 52 88 68 80 48 dc 0d 12 90 34 8b 5b f2 00 0c | ..E....q.y.......R.h.H....4.[... |
| 3c20 | 05 2a 88 01 d8 1a 1e 89 0f 88 06 90 07 d8 0b 0c 88 74 8a 38 d8 16 26 a0 71 d1 16 29 88 47 d8 0b | .*...............t.8..&.q..).G.. |
| 3c40 | 0c 88 73 8a 37 d8 15 24 a0 51 d1 15 27 88 46 d8 0b 11 90 41 8a 3a 98 17 a0 31 9a 1b d9 13 18 d8 | ..s.7..$.Q..'.F....A.:...1...... |
| 3c60 | 1f 24 a0 76 99 7e a8 76 b8 07 d1 2f 3f c4 13 c0 55 c8 46 d3 41 53 90 75 88 76 88 05 d8 0b 11 90 | .$.v.~.v.../?...U.F.AS.u.v...... |
| 3c80 | 41 8a 3a d8 0c 14 8f 4f 89 4f 98 52 a0 27 99 5c a8 32 b0 06 a9 3b d0 1c 37 d5 0c 38 d8 0d 14 90 | A.:....O.O.R.'.\.2...;..7..8.... |
| 3ca0 | 71 8b 5b d8 0c 14 8f 4f 89 4f 98 42 a0 17 99 4c d5 0c 29 f0 19 0c 05 2a f0 1a 00 08 0d 90 06 82 | q.[....O.O.B...L..)....*........ |
| 3cc0 | 7f d8 0f 14 dc 04 09 87 4d 81 4d 90 28 d4 04 1b dc 04 09 87 4d 81 4d 90 28 d4 04 1b e0 10 16 88 | ........M.M.(.......M.M.(....... |
| 3ce0 | 78 98 35 a0 31 99 39 d1 0f 25 80 48 e2 0a 12 e4 1c 21 9f 4d 99 4d a8 28 d3 1c 33 d1 08 19 88 17 | x.5.1.9..%.H.....!.M.M.(..3..... |
| 3d00 | 90 26 d8 08 0e 90 22 89 0c 88 06 d8 0b 11 94 43 98 08 93 4d a4 43 a8 08 a3 4d d1 14 31 d2 0b 31 | .&...."........C...M.C...M..1..1 |
| 3d20 | d8 13 18 f0 06 00 11 12 88 05 dc 11 16 90 76 93 1d f2 00 0b 09 1b 88 41 d9 0f 17 a1 18 a8 58 b0 | ..............v........A......X. |
| 3d40 | 61 a9 5b b8 11 a9 5e b8 68 c0 71 b9 6b d2 2d 49 dc 1a 1f 9f 2d 99 2d a8 08 d3 1a 31 90 07 d8 19 | a.[...^.h.q.k.-I....-.-....1.... |
| 3d60 | 1a 91 06 e4 24 29 a7 4d a1 4d b0 28 d3 24 3b d1 10 21 90 17 98 26 d8 0f 16 98 21 8a 7c d9 17 1c | ....$).M.M.(.$;..!...&....!.|... |
| 3d80 | e0 0f 16 98 11 89 7b 98 51 8a 7f a0 26 a8 31 a3 2a d8 23 2a a8 51 a1 3b b0 06 d0 22 37 90 08 98 | ......{.Q...&.1.*.#*.Q.;..."7... |
| 3da0 | 15 91 0f d8 10 15 98 11 91 0a 91 05 f0 17 0b 09 1b f4 1c 00 12 17 90 75 93 1c f2 00 05 09 32 88 | .......................u......2. |
| 3dc0 | 41 d8 13 1b 98 41 91 3b 88 44 d8 0f 13 90 41 89 77 98 11 8a 7b dc 10 15 97 0e 91 0e 98 78 a8 14 | A....A.;.D....A.w...{........x.. |
| 3de0 | d5 10 2e e4 10 15 97 0e 91 0e 98 78 a8 14 a8 61 a9 17 d5 10 31 f0 0b 05 09 32 f0 0c 00 0c 13 90 | ...........x...a....1....2...... |
| 3e00 | 51 8a 3b dc 0c 11 8f 4e 89 4e 98 38 a0 57 d4 0c 2d f3 3d 00 0b 13 f0 3e 00 0c 10 f8 f4 7b 01 00 | Q.;....N.N.8.W..-.=....>.....{.. |
| 3e20 | 0c 0e d7 0b 1b d1 0b 1b f2 00 01 05 15 d9 0f 14 f0 03 01 05 15 fa 73 11 00 00 00 82 3e 49 12 00 | ......................s.....>I.. |
| 3e40 | c9 12 13 49 28 03 c9 27 01 49 28 03 29 01 72 0b 00 00 00 29 0d da 07 5f 5f 64 6f 63 5f 5f 72 40 | ...I(..'.I(.).r....)...__doc__r@ |
| 3e60 | 00 00 00 da 08 6e 65 74 77 6f 72 6b 78 72 0e 00 00 00 da 07 5f 5f 61 6c 6c 5f 5f da 0d 5f 64 69 | .....networkxr......__all__.._di |
| 3e80 | 73 70 61 74 63 68 61 62 6c 65 72 03 00 00 00 72 27 00 00 00 72 08 00 00 00 72 07 00 00 00 72 04 | spatchabler....r'...r....r....r. |
| 3ea0 | 00 00 00 72 05 00 00 00 72 06 00 00 00 a9 00 72 15 00 00 00 72 14 00 00 00 fa 08 3c 6d 6f 64 75 | ...r....r......r....r......<modu |
| 3ec0 | 6c 65 3e 72 5b 00 00 00 01 00 00 00 73 ed 00 00 00 f0 03 01 01 01 d9 00 24 e3 00 0c e3 00 15 f2 | le>r[.......s...........$....... |
| 3ee0 | 04 07 0b 02 80 07 f0 14 00 02 12 80 12 d7 01 11 d1 01 11 98 14 d4 01 1e f2 02 37 01 11 f3 03 00 | ..........................7..... |
| 3f00 | 02 1f f0 02 37 01 11 f2 74 01 11 01 29 f0 28 00 02 12 80 12 d7 01 11 d1 01 11 98 14 d4 01 1e f1 | ....7...t...).(................. |
| 3f20 | 02 56 01 01 10 f3 03 00 02 1f f0 02 56 01 01 10 f0 72 02 00 02 12 80 12 d7 01 11 d1 01 11 98 14 | .V..........V....r.............. |
| 3f40 | d4 01 1e f1 02 57 01 01 10 f3 03 00 02 1f f0 02 57 01 01 10 f0 74 02 00 02 12 80 12 d7 01 11 d1 | .....W..........W....t.......... |
| 3f60 | 01 11 98 14 d4 01 1e f1 02 2f 01 10 f3 03 00 02 1f f0 02 2f 01 10 f0 64 01 00 02 12 80 12 d7 01 | ........./........./...d........ |
| 3f80 | 11 d1 01 11 98 14 d4 01 1e f1 02 2b 01 41 01 f3 03 00 02 1f f0 02 2b 01 41 01 f0 5c 01 00 02 12 | ...........+.A........+.A..\.... |
| 3fa0 | 80 12 d7 01 11 d1 01 11 98 14 d4 01 1e f1 02 6b 01 01 10 f3 03 00 02 1f f1 02 6b 01 01 10 72 15 | ...............k..........k...r. |
| 3fc0 | 00 00 00 | ... |
 |
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/algorithms/__pycache__/graphical.cpython-312.pyc
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