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2500 74 20 69 73 20 6e 6f 74 20 73 70 65 63 69 66 69 65 64 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 t.is.not.specified.then.........
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2540 20 69 73 20 75 73 65 64 2e 0a 0a 20 20 20 20 65 64 67 65 5f 73 75 62 73 74 5f 63 6f 73 74 2c 20 .is.used.......edge_subst_cost,.
2560 65 64 67 65 5f 64 65 6c 5f 63 6f 73 74 2c 20 65 64 67 65 5f 69 6e 73 5f 63 6f 73 74 20 3a 20 63 edge_del_cost,.edge_ins_cost.:.c
2580 61 6c 6c 61 62 6c 65 0a 20 20 20 20 20 20 20 20 46 75 6e 63 74 69 6f 6e 73 20 74 68 61 74 20 72 allable.........Functions.that.r
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25e0 20 65 64 67 65 20 69 6e 73 65 72 74 69 6f 6e 2c 20 72 65 73 70 65 63 74 69 76 65 6c 79 2e 0a 0a .edge.insertion,.respectively...
2600 20 20 20 20 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 73 20 77 69 6c 6c 20 62 65 20 63 61 ........The.functions.will.be.ca
2620 6c 6c 65 64 20 6c 69 6b 65 0a 0a 20 20 20 20 20 20 20 20 20 20 20 65 64 67 65 5f 73 75 62 73 74 lled.like.............edge_subst
2640 5f 63 6f 73 74 28 47 31 5b 75 31 5d 5b 76 31 5d 2c 20 47 32 5b 75 32 5d 5b 76 32 5d 29 2c 0a 20 _cost(G1[u1][v1],.G2[u2][v2]),..
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26a0 5b 75 32 5d 5b 76 32 5d 29 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 61 74 20 69 73 2c 20 74 68 65 [u2][v2])...........That.is,.the
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2720 70 65 63 74 65 64 20 74 6f 20 72 65 74 75 72 6e 0a 20 20 20 20 20 20 20 20 70 6f 73 69 74 69 76 pected.to.return.........positiv
2740 65 20 6e 75 6d 65 72 69 63 20 76 61 6c 75 65 73 2e 0a 0a 20 20 20 20 20 20 20 20 46 75 6e 63 74 e.numeric.values...........Funct
2760 69 6f 6e 20 65 64 67 65 5f 73 75 62 73 74 5f 63 6f 73 74 20 6f 76 65 72 72 69 64 65 73 20 65 64 ion.edge_subst_cost.overrides.ed
2780 67 65 5f 6d 61 74 63 68 20 69 66 20 73 70 65 63 69 66 69 65 64 2e 0a 20 20 20 20 20 20 20 20 49 ge_match.if.specified..........I
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27c0 62 73 74 5f 63 6f 73 74 20 61 72 65 20 73 70 65 63 69 66 69 65 64 20 74 68 65 6e 0a 20 20 20 20 bst_cost.are.specified.then.....
27e0 20 20 20 20 64 65 66 61 75 6c 74 20 65 64 67 65 20 73 75 62 73 74 69 74 75 74 69 6f 6e 20 63 6f ....default.edge.substitution.co
2800 73 74 20 6f 66 20 30 20 69 73 20 75 73 65 64 20 28 65 64 67 65 20 61 74 74 72 69 62 75 74 65 73 st.of.0.is.used.(edge.attributes
2820 0a 20 20 20 20 20 20 20 20 61 72 65 20 6e 6f 74 20 63 6f 6e 73 69 64 65 72 65 64 20 64 75 72 69 .........are.not.considered.duri
2840 6e 67 20 6d 61 74 63 68 69 6e 67 29 2e 0a 0a 20 20 20 20 20 20 20 20 49 66 20 65 64 67 65 5f 64 ng.matching)...........If.edge_d
2860 65 6c 5f 63 6f 73 74 20 69 73 20 6e 6f 74 20 73 70 65 63 69 66 69 65 64 20 74 68 65 6e 20 64 65 el_cost.is.not.specified.then.de
2880 66 61 75 6c 74 20 65 64 67 65 20 64 65 6c 65 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 63 6f 73 74 fault.edge.deletion.........cost
28a0 20 6f 66 20 31 20 69 73 20 75 73 65 64 2e 20 20 49 66 20 65 64 67 65 5f 69 6e 73 5f 63 6f 73 74 .of.1.is.used...If.edge_ins_cost
28c0 20 69 73 20 6e 6f 74 20 73 70 65 63 69 66 69 65 64 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 64 .is.not.specified.then.........d
28e0 65 66 61 75 6c 74 20 65 64 67 65 20 69 6e 73 65 72 74 69 6f 6e 20 63 6f 73 74 20 6f 66 20 31 20 efault.edge.insertion.cost.of.1.
2900 69 73 20 75 73 65 64 2e 0a 0a 20 20 20 20 75 70 70 65 72 5f 62 6f 75 6e 64 20 3a 20 6e 75 6d 65 is.used.......upper_bound.:.nume
2920 72 69 63 0a 20 20 20 20 20 20 20 20 4d 61 78 69 6d 75 6d 20 65 64 69 74 20 64 69 73 74 61 6e 63 ric.........Maximum.edit.distanc
2940 65 20 74 6f 20 63 6f 6e 73 69 64 65 72 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 20 20 20 e.to.consider.......Returns.....
2960 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 65 64 69 74 5f 70 61 74 68 73 20 3a 20 6c 69 73 74 20 6f 66 -------.....edit_paths.:.list.of
2980 20 74 75 70 6c 65 73 20 28 6e 6f 64 65 5f 65 64 69 74 5f 70 61 74 68 2c 20 65 64 67 65 5f 65 64 .tuples.(node_edit_path,.edge_ed
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29c0 20 3a 20 6c 69 73 74 20 6f 66 20 74 75 70 6c 65 73 20 60 60 28 75 2c 20 76 29 60 60 20 69 6e 64 .:.list.of.tuples.``(u,.v)``.ind
29e0 69 63 61 74 69 6e 67 20 6e 6f 64 65 20 74 72 61 6e 73 66 6f 72 6d 61 74 69 6f 6e 73 0a 20 20 20 icating.node.transformations....
2a00 20 20 20 20 20 20 62 65 74 77 65 65 6e 20 60 47 31 60 20 61 6e 64 20 60 47 32 60 2e 20 60 60 75 ......between.`G1`.and.`G2`..``u
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2a80 74 20 6f 66 20 74 75 70 6c 65 73 20 60 60 28 28 75 31 2c 20 76 31 29 2c 20 28 75 32 2c 20 76 32 t.of.tuples.``((u1,.v1),.(u2,.v2
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2ae0 47 32 60 2e 20 60 60 28 4e 6f 6e 65 2c 20 28 75 32 2c 76 32 29 29 60 60 20 66 6f 72 20 69 6e 73 G2`..``(None,.(u2,v2))``.for.ins
2b00 65 72 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 20 61 6e 64 20 60 60 28 28 75 31 2c 76 31 29 2c 20 ertion..........and.``((u1,v1),.
2b20 4e 6f 6e 65 29 60 60 20 66 6f 72 20 64 65 6c 65 74 69 6f 6e 2e 0a 0a 20 20 20 20 63 6f 73 74 20 None)``.for.deletion.......cost.
2b40 3a 20 6e 75 6d 65 72 69 63 0a 20 20 20 20 20 20 20 20 4f 70 74 69 6d 61 6c 20 65 64 69 74 20 70 :.numeric.........Optimal.edit.p
2b60 61 74 68 20 63 6f 73 74 20 28 67 72 61 70 68 20 65 64 69 74 20 64 69 73 74 61 6e 63 65 29 2e 20 ath.cost.(graph.edit.distance)..
2b80 57 68 65 6e 20 74 68 65 20 63 6f 73 74 0a 20 20 20 20 20 20 20 20 69 73 20 7a 65 72 6f 2c 20 69 When.the.cost.........is.zero,.i
2ba0 74 20 69 6e 64 69 63 61 74 65 73 20 74 68 61 74 20 60 47 31 60 20 61 6e 64 20 60 47 32 60 20 61 t.indicates.that.`G1`.and.`G2`.a
2bc0 72 65 20 69 73 6f 6d 6f 72 70 68 69 63 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 re.isomorphic.......Examples....
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2c00 67 72 61 70 68 28 34 29 0a 20 20 20 20 3e 3e 3e 20 47 32 20 3d 20 6e 78 2e 77 68 65 65 6c 5f 67 graph(4).....>>>.G2.=.nx.wheel_g
2c20 72 61 70 68 28 35 29 0a 20 20 20 20 3e 3e 3e 20 70 61 74 68 73 2c 20 63 6f 73 74 20 3d 20 6e 78 raph(5).....>>>.paths,.cost.=.nx
2c40 2e 6f 70 74 69 6d 61 6c 5f 65 64 69 74 5f 70 61 74 68 73 28 47 31 2c 20 47 32 29 0a 20 20 20 20 .optimal_edit_paths(G1,.G2).....
2c60 3e 3e 3e 20 6c 65 6e 28 70 61 74 68 73 29 0a 20 20 20 20 34 30 0a 20 20 20 20 3e 3e 3e 20 63 6f >>>.len(paths).....40.....>>>.co
2c80 73 74 0a 20 20 20 20 35 2e 30 0a 0a 20 20 20 20 4e 6f 74 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 0a st.....5.0......Notes.....-----.
2ca0 20 20 20 20 54 6f 20 74 72 61 6e 73 66 6f 72 6d 20 60 47 31 60 20 69 6e 74 6f 20 61 20 67 72 61 ....To.transform.`G1`.into.a.gra
2cc0 70 68 20 69 73 6f 6d 6f 72 70 68 69 63 20 74 6f 20 60 47 32 60 2c 20 61 70 70 6c 79 20 74 68 65 ph.isomorphic.to.`G2`,.apply.the
2ce0 20 6e 6f 64 65 0a 20 20 20 20 61 6e 64 20 65 64 67 65 20 65 64 69 74 73 20 69 6e 20 74 68 65 20 .node.....and.edge.edits.in.the.
2d00 72 65 74 75 72 6e 65 64 20 60 60 65 64 69 74 5f 70 61 74 68 73 60 60 2e 0a 20 20 20 20 49 6e 20 returned.``edit_paths``......In.
2d20 74 68 65 20 63 61 73 65 20 6f 66 20 69 73 6f 6d 6f 72 70 68 69 63 20 67 72 61 70 68 73 2c 20 74 the.case.of.isomorphic.graphs,.t
2d40 68 65 20 63 6f 73 74 20 69 73 20 7a 65 72 6f 2c 20 61 6e 64 20 74 68 65 20 70 61 74 68 73 0a 20 he.cost.is.zero,.and.the.paths..
2d60 20 20 20 72 65 70 72 65 73 65 6e 74 20 64 69 66 66 65 72 65 6e 74 20 69 73 6f 6d 6f 72 70 68 69 ...represent.different.isomorphi
2d80 63 20 6d 61 70 70 69 6e 67 73 20 28 69 73 6f 6d 6f 72 70 68 69 73 6d 73 29 2e 20 54 68 61 74 20 c.mappings.(isomorphisms)..That.
2da0 69 73 2c 20 74 68 65 0a 20 20 20 20 65 64 69 74 73 20 69 6e 76 6f 6c 76 65 20 72 65 6e 61 6d 69 is,.the.....edits.involve.renami
2dc0 6e 67 20 6e 6f 64 65 73 20 61 6e 64 20 65 64 67 65 73 20 74 6f 20 6d 61 74 63 68 20 74 68 65 20 ng.nodes.and.edges.to.match.the.
2de0 73 74 72 75 63 74 75 72 65 20 6f 66 20 60 47 32 60 2e 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f structure.of.`G2`.......See.Also
2e00 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 67 72 61 70 68 5f 65 64 69 74 5f 64 69 73 .....--------.....graph_edit_dis
2e20 74 61 6e 63 65 2c 20 6f 70 74 69 6d 69 7a 65 5f 65 64 69 74 5f 70 61 74 68 73 0a 0a 20 20 20 20 tance,.optimize_edit_paths......
2e40 52 65 66 65 72 65 6e 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 2e 2e References.....----------.......
2e60 20 5b 31 5d 20 5a 65 69 6e 61 20 41 62 75 2d 41 69 73 68 65 68 2c 20 52 6f 6d 61 69 6e 20 52 61 .[1].Zeina.Abu-Aisheh,.Romain.Ra
2e80 76 65 61 75 78 2c 20 4a 65 61 6e 2d 59 76 65 73 20 52 61 6d 65 6c 2c 20 50 61 74 72 69 63 6b 0a veaux,.Jean-Yves.Ramel,.Patrick.
2ea0 20 20 20 20 20 20 20 4d 61 72 74 69 6e 65 61 75 2e 20 41 6e 20 45 78 61 63 74 20 47 72 61 70 68 .......Martineau..An.Exact.Graph
2ec0 20 45 64 69 74 20 44 69 73 74 61 6e 63 65 20 41 6c 67 6f 72 69 74 68 6d 20 66 6f 72 20 53 6f 6c .Edit.Distance.Algorithm.for.Sol
2ee0 76 69 6e 67 0a 20 20 20 20 20 20 20 50 61 74 74 65 72 6e 20 52 65 63 6f 67 6e 69 74 69 6f 6e 20 ving........Pattern.Recognition.
2f00 50 72 6f 62 6c 65 6d 73 2e 20 34 74 68 20 49 6e 74 65 72 6e 61 74 69 6f 6e 61 6c 20 43 6f 6e 66 Problems..4th.International.Conf
2f20 65 72 65 6e 63 65 20 6f 6e 0a 20 20 20 20 20 20 20 50 61 74 74 65 72 6e 20 52 65 63 6f 67 6e 69 erence.on........Pattern.Recogni
2f40 74 69 6f 6e 20 41 70 70 6c 69 63 61 74 69 6f 6e 73 20 61 6e 64 20 4d 65 74 68 6f 64 73 20 32 30 tion.Applications.and.Methods.20
2f60 31 35 2c 20 4a 61 6e 20 32 30 31 35 2c 0a 20 20 20 20 20 20 20 4c 69 73 62 6f 6e 2c 20 50 6f 72 15,.Jan.2015,........Lisbon,.Por
2f80 74 75 67 61 6c 2e 20 32 30 31 35 2c 0a 20 20 20 20 20 20 20 3c 31 30 2e 35 32 32 30 2f 30 30 30 tugal..2015,........<10.5220/000
2fa0 35 32 30 39 32 30 32 37 31 30 32 37 38 3e 2e 20 3c 68 61 6c 2d 30 31 31 36 38 38 31 36 3e 0a 20 5209202710278>..<hal-01168816>..
2fc0 20 20 20 20 20 20 68 74 74 70 73 3a 2f 2f 68 61 6c 2e 61 72 63 68 69 76 65 73 2d 6f 75 76 65 72 ......https://hal.archives-ouver
2fe0 74 65 73 2e 66 72 2f 68 61 6c 2d 30 31 31 36 38 38 31 36 0a 0a 20 20 20 20 4e 46 29 02 72 09 00 tes.fr/hal-01168816......NF).r..
3000 00 00 da 06 61 70 70 65 6e 64 29 10 72 0e 00 00 00 72 0f 00 00 00 72 15 00 00 00 72 16 00 00 00 ....append).r....r....r....r....
3020 72 17 00 00 00 72 18 00 00 00 72 19 00 00 00 72 1a 00 00 00 72 1b 00 00 00 72 1c 00 00 00 72 1e r....r....r....r....r....r....r.
3040 00 00 00 da 05 70 61 74 68 73 72 20 00 00 00 da 0b 76 65 72 74 65 78 5f 70 61 74 68 da 09 65 64 .....pathsr......vertex_path..ed
3060 67 65 5f 70 61 74 68 72 22 00 00 00 73 10 00 00 00 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 ge_pathr"...s...................
3080 20 72 23 00 00 00 72 07 00 00 00 72 07 00 00 00 d2 00 00 00 73 83 00 00 00 80 00 f0 70 04 00 0d .r#...r....r........s.......p...
30a0 0f 80 45 d8 0f 13 80 48 dc 28 3b d8 08 0a d8 08 0a d8 08 12 d8 08 12 d8 08 17 d8 08 15 d8 08 15 ..E....H.(;.....................
30c0 d8 08 17 d8 08 15 d8 08 15 d8 08 13 d8 08 0d f3 19 0d 29 06 f2 00 12 05 18 d1 08 24 88 0b 90 59 ..................)........$...Y
30e0 a0 04 f0 1e 00 0c 14 d0 0b 1f a0 44 a8 38 a2 4f d8 14 16 88 45 d8 08 0d 8f 0c 89 0c 90 6b a0 39 ...........D.8.O....E........k.9
3100 d0 15 2d d4 08 2e d8 13 17 89 08 f0 25 12 05 18 f0 26 00 0c 11 90 28 88 3f d0 04 1a 72 24 00 00 ..-.........%....&....(.?...r$..
3120 00 63 0b 00 00 00 00 00 00 00 00 00 00 00 0e 00 00 00 23 00 00 00 f3 52 00 00 00 4b 00 01 00 97 .c................#....R...K....
3140 00 74 01 00 00 00 00 00 00 00 00 7c 00 7c 01 7c 02 7c 03 7c 04 7c 05 7c 06 7c 07 7c 08 7c 09 7c .t.........|.|.|.|.|.|.|.|.|.|.|
3160 0a 64 01 ab 0c 00 00 00 00 00 00 44 00 5d 0a 00 00 5c 03 00 00 7d 0b 7d 0b 7d 0c 7c 0c 96 01 97 .d.........D.]...\...}.}.}.|....
3180 01 01 00 8c 0c 04 00 79 02 ad 03 77 01 29 03 61 fd 10 00 00 52 65 74 75 72 6e 73 20 63 6f 6e 73 .......y...w.).a....Returns.cons
31a0 65 63 75 74 69 76 65 20 61 70 70 72 6f 78 69 6d 61 74 69 6f 6e 73 20 6f 66 20 47 45 44 20 28 67 ecutive.approximations.of.GED.(g
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31e0 67 72 61 70 68 73 20 47 31 20 61 6e 64 20 47 32 2e 0a 0a 20 20 20 20 47 72 61 70 68 20 65 64 69 graphs.G1.and.G2.......Graph.edi
3200 74 20 64 69 73 74 61 6e 63 65 20 69 73 20 61 20 67 72 61 70 68 20 73 69 6d 69 6c 61 72 69 74 79 t.distance.is.a.graph.similarity
3220 20 6d 65 61 73 75 72 65 20 61 6e 61 6c 6f 67 6f 75 73 20 74 6f 0a 20 20 20 20 4c 65 76 65 6e 73 .measure.analogous.to.....Levens
3240 68 74 65 69 6e 20 64 69 73 74 61 6e 63 65 20 66 6f 72 20 73 74 72 69 6e 67 73 2e 20 20 49 74 20 htein.distance.for.strings...It.
3260 69 73 20 64 65 66 69 6e 65 64 20 61 73 20 6d 69 6e 69 6d 75 6d 20 63 6f 73 74 0a 20 20 20 20 6f is.defined.as.minimum.cost.....o
3280 66 20 65 64 69 74 20 70 61 74 68 20 28 73 65 71 75 65 6e 63 65 20 6f 66 20 6e 6f 64 65 20 61 6e f.edit.path.(sequence.of.node.an
32a0 64 20 65 64 67 65 20 65 64 69 74 20 6f 70 65 72 61 74 69 6f 6e 73 29 0a 20 20 20 20 74 72 61 6e d.edge.edit.operations).....tran
32c0 73 66 6f 72 6d 69 6e 67 20 67 72 61 70 68 20 47 31 20 74 6f 20 67 72 61 70 68 20 69 73 6f 6d 6f sforming.graph.G1.to.graph.isomo
32e0 72 70 68 69 63 20 74 6f 20 47 32 2e 0a 0a 20 20 20 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 rphic.to.G2.......Parameters....
3300 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 31 2c 20 47 32 3a 20 67 72 61 70 68 73 0a 20 .----------.....G1,.G2:.graphs..
3320 20 20 20 20 20 20 20 54 68 65 20 74 77 6f 20 67 72 61 70 68 73 20 47 31 20 61 6e 64 20 47 32 20 .......The.two.graphs.G1.and.G2.
3340 6d 75 73 74 20 62 65 20 6f 66 20 74 68 65 20 73 61 6d 65 20 74 79 70 65 2e 0a 0a 20 20 20 20 6e must.be.of.the.same.type.......n
3360 6f 64 65 5f 6d 61 74 63 68 20 3a 20 63 61 6c 6c 61 62 6c 65 0a 20 20 20 20 20 20 20 20 41 20 66 ode_match.:.callable.........A.f
3380 75 6e 63 74 69 6f 6e 20 74 68 61 74 20 72 65 74 75 72 6e 73 20 54 72 75 65 20 69 66 20 6e 6f 64 unction.that.returns.True.if.nod
33a0 65 20 6e 31 20 69 6e 20 47 31 20 61 6e 64 20 6e 32 20 69 6e 20 47 32 0a 20 20 20 20 20 20 20 20 e.n1.in.G1.and.n2.in.G2.........
33c0 73 68 6f 75 6c 64 20 62 65 20 63 6f 6e 73 69 64 65 72 65 64 20 65 71 75 61 6c 20 64 75 72 69 6e should.be.considered.equal.durin
33e0 67 20 6d 61 74 63 68 69 6e 67 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f g.matching...........The.functio
3400 6e 20 77 69 6c 6c 20 62 65 20 63 61 6c 6c 65 64 20 6c 69 6b 65 0a 0a 20 20 20 20 20 20 20 20 20 n.will.be.called.like...........
3420 20 20 6e 6f 64 65 5f 6d 61 74 63 68 28 47 31 2e 6e 6f 64 65 73 5b 6e 31 5d 2c 20 47 32 2e 6e 6f ..node_match(G1.nodes[n1],.G2.no
3440 64 65 73 5b 6e 32 5d 29 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 61 74 20 69 73 2c 20 74 68 65 20 des[n2])...........That.is,.the.
3460 66 75 6e 63 74 69 6f 6e 20 77 69 6c 6c 20 72 65 63 65 69 76 65 20 74 68 65 20 6e 6f 64 65 20 61 function.will.receive.the.node.a
3480 74 74 72 69 62 75 74 65 0a 20 20 20 20 20 20 20 20 64 69 63 74 69 6f 6e 61 72 69 65 73 20 66 6f ttribute.........dictionaries.fo
34a0 72 20 6e 31 20 61 6e 64 20 6e 32 20 61 73 20 69 6e 70 75 74 73 2e 0a 0a 20 20 20 20 20 20 20 20 r.n1.and.n2.as.inputs...........
34c0 49 67 6e 6f 72 65 64 20 69 66 20 6e 6f 64 65 5f 73 75 62 73 74 5f 63 6f 73 74 20 69 73 20 73 70 Ignored.if.node_subst_cost.is.sp
34e0 65 63 69 66 69 65 64 2e 20 20 49 66 20 6e 65 69 74 68 65 72 0a 20 20 20 20 20 20 20 20 6e 6f 64 ecified...If.neither.........nod
3500 65 5f 6d 61 74 63 68 20 6e 6f 72 20 6e 6f 64 65 5f 73 75 62 73 74 5f 63 6f 73 74 20 61 72 65 20 e_match.nor.node_subst_cost.are.
3520 73 70 65 63 69 66 69 65 64 20 74 68 65 6e 20 6e 6f 64 65 0a 20 20 20 20 20 20 20 20 61 74 74 72 specified.then.node.........attr
3540 69 62 75 74 65 73 20 61 72 65 20 6e 6f 74 20 63 6f 6e 73 69 64 65 72 65 64 2e 0a 0a 20 20 20 20 ibutes.are.not.considered.......
3560 65 64 67 65 5f 6d 61 74 63 68 20 3a 20 63 61 6c 6c 61 62 6c 65 0a 20 20 20 20 20 20 20 20 41 20 edge_match.:.callable.........A.
3580 66 75 6e 63 74 69 6f 6e 20 74 68 61 74 20 72 65 74 75 72 6e 73 20 54 72 75 65 20 69 66 20 74 68 function.that.returns.True.if.th
35a0 65 20 65 64 67 65 20 61 74 74 72 69 62 75 74 65 20 64 69 63 74 69 6f 6e 61 72 69 65 73 0a 20 20 e.edge.attribute.dictionaries...
35c0 20 20 20 20 20 20 66 6f 72 20 74 68 65 20 70 61 69 72 20 6f 66 20 6e 6f 64 65 73 20 28 75 31 2c ......for.the.pair.of.nodes.(u1,
35e0 20 76 31 29 20 69 6e 20 47 31 20 61 6e 64 20 28 75 32 2c 20 76 32 29 20 69 6e 20 47 32 20 73 68 .v1).in.G1.and.(u2,.v2).in.G2.sh
3600 6f 75 6c 64 0a 20 20 20 20 20 20 20 20 62 65 20 63 6f 6e 73 69 64 65 72 65 64 20 65 71 75 61 6c ould.........be.considered.equal
3620 20 64 75 72 69 6e 67 20 6d 61 74 63 68 69 6e 67 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 66 .during.matching...........The.f
3640 75 6e 63 74 69 6f 6e 20 77 69 6c 6c 20 62 65 20 63 61 6c 6c 65 64 20 6c 69 6b 65 0a 0a 20 20 20 unction.will.be.called.like.....
3660 20 20 20 20 20 20 20 20 65 64 67 65 5f 6d 61 74 63 68 28 47 31 5b 75 31 5d 5b 76 31 5d 2c 20 47 ........edge_match(G1[u1][v1],.G
3680 32 5b 75 32 5d 5b 76 32 5d 29 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 61 74 20 69 73 2c 20 74 68 2[u2][v2])...........That.is,.th
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36c0 20 61 74 74 72 69 62 75 74 65 0a 20 20 20 20 20 20 20 20 64 69 63 74 69 6f 6e 61 72 69 65 73 20 .attribute.........dictionaries.
36e0 6f 66 20 74 68 65 20 65 64 67 65 73 20 75 6e 64 65 72 20 63 6f 6e 73 69 64 65 72 61 74 69 6f 6e of.the.edges.under.consideration
3700 2e 0a 0a 20 20 20 20 20 20 20 20 49 67 6e 6f 72 65 64 20 69 66 20 65 64 67 65 5f 73 75 62 73 74 ...........Ignored.if.edge_subst
3720 5f 63 6f 73 74 20 69 73 20 73 70 65 63 69 66 69 65 64 2e 20 20 49 66 20 6e 65 69 74 68 65 72 0a _cost.is.specified...If.neither.
3740 20 20 20 20 20 20 20 20 65 64 67 65 5f 6d 61 74 63 68 20 6e 6f 72 20 65 64 67 65 5f 73 75 62 73 ........edge_match.nor.edge_subs
3760 74 5f 63 6f 73 74 20 61 72 65 20 73 70 65 63 69 66 69 65 64 20 74 68 65 6e 20 65 64 67 65 0a 20 t_cost.are.specified.then.edge..
3780 20 20 20 20 20 20 20 61 74 74 72 69 62 75 74 65 73 20 61 72 65 20 6e 6f 74 20 63 6f 6e 73 69 64 .......attributes.are.not.consid
37a0 65 72 65 64 2e 0a 0a 20 20 20 20 6e 6f 64 65 5f 73 75 62 73 74 5f 63 6f 73 74 2c 20 6e 6f 64 65 ered.......node_subst_cost,.node
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37e0 62 6c 65 0a 20 20 20 20 20 20 20 20 46 75 6e 63 74 69 6f 6e 73 20 74 68 61 74 20 72 65 74 75 72 ble.........Functions.that.retur
3800 6e 20 74 68 65 20 63 6f 73 74 73 20 6f 66 20 6e 6f 64 65 20 73 75 62 73 74 69 74 75 74 69 6f 6e n.the.costs.of.node.substitution
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3860 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 73 20 77 69 6c 6c 20 62 65 20 63 61 6c 6c 65 64 ....The.functions.will.be.called
3880 20 6c 69 6b 65 0a 0a 20 20 20 20 20 20 20 20 20 20 20 6e 6f 64 65 5f 73 75 62 73 74 5f 63 6f 73 .like.............node_subst_cos
38a0 74 28 47 31 2e 6e 6f 64 65 73 5b 6e 31 5d 2c 20 47 32 2e 6e 6f 64 65 73 5b 6e 32 5d 29 2c 0a 20 t(G1.nodes[n1],.G2.nodes[n2]),..
38c0 20 20 20 20 20 20 20 20 20 20 6e 6f 64 65 5f 64 65 6c 5f 63 6f 73 74 28 47 31 2e 6e 6f 64 65 73 ..........node_del_cost(G1.nodes
38e0 5b 6e 31 5d 29 2c 0a 20 20 20 20 20 20 20 20 20 20 20 6e 6f 64 65 5f 69 6e 73 5f 63 6f 73 74 28 [n1]),............node_ins_cost(
3900 47 32 2e 6e 6f 64 65 73 5b 6e 32 5d 29 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 61 74 20 69 73 2c G2.nodes[n2])...........That.is,
3920 20 74 68 65 20 66 75 6e 63 74 69 6f 6e 73 20 77 69 6c 6c 20 72 65 63 65 69 76 65 20 74 68 65 20 .the.functions.will.receive.the.
3940 6e 6f 64 65 20 61 74 74 72 69 62 75 74 65 0a 20 20 20 20 20 20 20 20 64 69 63 74 69 6f 6e 61 72 node.attribute.........dictionar
3960 69 65 73 20 61 73 20 69 6e 70 75 74 73 2e 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 73 20 61 72 ies.as.inputs...The.functions.ar
3980 65 20 65 78 70 65 63 74 65 64 20 74 6f 20 72 65 74 75 72 6e 0a 20 20 20 20 20 20 20 20 70 6f 73 e.expected.to.return.........pos
39a0 69 74 69 76 65 20 6e 75 6d 65 72 69 63 20 76 61 6c 75 65 73 2e 0a 0a 20 20 20 20 20 20 20 20 46 itive.numeric.values...........F
39c0 75 6e 63 74 69 6f 6e 20 6e 6f 64 65 5f 73 75 62 73 74 5f 63 6f 73 74 20 6f 76 65 72 72 69 64 65 unction.node_subst_cost.override
39e0 73 20 6e 6f 64 65 5f 6d 61 74 63 68 20 69 66 20 73 70 65 63 69 66 69 65 64 2e 0a 20 20 20 20 20 s.node_match.if.specified.......
3a00 20 20 20 49 66 20 6e 65 69 74 68 65 72 20 6e 6f 64 65 5f 6d 61 74 63 68 20 6e 6f 72 20 6e 6f 64 ...If.neither.node_match.nor.nod
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3a40 20 20 20 20 20 20 20 20 64 65 66 61 75 6c 74 20 6e 6f 64 65 20 73 75 62 73 74 69 74 75 74 69 6f ........default.node.substitutio
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3ae0 6e 20 64 65 66 61 75 6c 74 20 6e 6f 64 65 20 64 65 6c 65 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 n.default.node.deletion.........
3b00 63 6f 73 74 20 6f 66 20 31 20 69 73 20 75 73 65 64 2e 20 20 49 66 20 6e 6f 64 65 5f 69 6e 73 5f cost.of.1.is.used...If.node_ins_
3b20 63 6f 73 74 20 69 73 20 6e 6f 74 20 73 70 65 63 69 66 69 65 64 20 74 68 65 6e 0a 20 20 20 20 20 cost.is.not.specified.then......
3b40 20 20 20 64 65 66 61 75 6c 74 20 6e 6f 64 65 20 69 6e 73 65 72 74 69 6f 6e 20 63 6f 73 74 20 6f ...default.node.insertion.cost.o
3b60 66 20 31 20 69 73 20 75 73 65 64 2e 0a 0a 20 20 20 20 65 64 67 65 5f 73 75 62 73 74 5f 63 6f 73 f.1.is.used.......edge_subst_cos
3b80 74 2c 20 65 64 67 65 5f 64 65 6c 5f 63 6f 73 74 2c 20 65 64 67 65 5f 69 6e 73 5f 63 6f 73 74 20 t,.edge_del_cost,.edge_ins_cost.
3ba0 3a 20 63 61 6c 6c 61 62 6c 65 0a 20 20 20 20 20 20 20 20 46 75 6e 63 74 69 6f 6e 73 20 74 68 61 :.callable.........Functions.tha
3bc0 74 20 72 65 74 75 72 6e 20 74 68 65 20 63 6f 73 74 73 20 6f 66 20 65 64 67 65 20 73 75 62 73 74 t.return.the.costs.of.edge.subst
3be0 69 74 75 74 69 6f 6e 2c 20 65 64 67 65 0a 20 20 20 20 20 20 20 20 64 65 6c 65 74 69 6f 6e 2c 20 itution,.edge.........deletion,.
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3c20 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 73 20 77 69 6c 6c 20 62 65 ...........The.functions.will.be
3c40 20 63 61 6c 6c 65 64 20 6c 69 6b 65 0a 0a 20 20 20 20 20 20 20 20 20 20 20 65 64 67 65 5f 73 75 .called.like.............edge_su
3c60 62 73 74 5f 63 6f 73 74 28 47 31 5b 75 31 5d 5b 76 31 5d 2c 20 47 32 5b 75 32 5d 5b 76 32 5d 29 bst_cost(G1[u1][v1],.G2[u2][v2])
3c80 2c 0a 20 20 20 20 20 20 20 20 20 20 20 65 64 67 65 5f 64 65 6c 5f 63 6f 73 74 28 47 31 5b 75 31 ,............edge_del_cost(G1[u1
3ca0 5d 5b 76 31 5d 29 2c 0a 20 20 20 20 20 20 20 20 20 20 20 65 64 67 65 5f 69 6e 73 5f 63 6f 73 74 ][v1]),............edge_ins_cost
3cc0 28 47 32 5b 75 32 5d 5b 76 32 5d 29 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 61 74 20 69 73 2c 20 (G2[u2][v2])...........That.is,.
3ce0 74 68 65 20 66 75 6e 63 74 69 6f 6e 73 20 77 69 6c 6c 20 72 65 63 65 69 76 65 20 74 68 65 20 65 the.functions.will.receive.the.e
3d00 64 67 65 20 61 74 74 72 69 62 75 74 65 0a 20 20 20 20 20 20 20 20 64 69 63 74 69 6f 6e 61 72 69 dge.attribute.........dictionari
3d20 65 73 20 61 73 20 69 6e 70 75 74 73 2e 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 73 20 61 72 65 es.as.inputs...The.functions.are
3d40 20 65 78 70 65 63 74 65 64 20 74 6f 20 72 65 74 75 72 6e 0a 20 20 20 20 20 20 20 20 70 6f 73 69 .expected.to.return.........posi
3d60 74 69 76 65 20 6e 75 6d 65 72 69 63 20 76 61 6c 75 65 73 2e 0a 0a 20 20 20 20 20 20 20 20 46 75 tive.numeric.values...........Fu
3d80 6e 63 74 69 6f 6e 20 65 64 67 65 5f 73 75 62 73 74 5f 63 6f 73 74 20 6f 76 65 72 72 69 64 65 73 nction.edge_subst_cost.overrides
3da0 20 65 64 67 65 5f 6d 61 74 63 68 20 69 66 20 73 70 65 63 69 66 69 65 64 2e 0a 20 20 20 20 20 20 .edge_match.if.specified........
3dc0 20 20 49 66 20 6e 65 69 74 68 65 72 20 65 64 67 65 5f 6d 61 74 63 68 20 6e 6f 72 20 65 64 67 65 ..If.neither.edge_match.nor.edge
3de0 5f 73 75 62 73 74 5f 63 6f 73 74 20 61 72 65 20 73 70 65 63 69 66 69 65 64 20 74 68 65 6e 0a 20 _subst_cost.are.specified.then..
3e00 20 20 20 20 20 20 20 64 65 66 61 75 6c 74 20 65 64 67 65 20 73 75 62 73 74 69 74 75 74 69 6f 6e .......default.edge.substitution
3e20 20 63 6f 73 74 20 6f 66 20 30 20 69 73 20 75 73 65 64 20 28 65 64 67 65 20 61 74 74 72 69 62 75 .cost.of.0.is.used.(edge.attribu
3e40 74 65 73 0a 20 20 20 20 20 20 20 20 61 72 65 20 6e 6f 74 20 63 6f 6e 73 69 64 65 72 65 64 20 64 tes.........are.not.considered.d
3e60 75 72 69 6e 67 20 6d 61 74 63 68 69 6e 67 29 2e 0a 0a 20 20 20 20 20 20 20 20 49 66 20 65 64 67 uring.matching)...........If.edg
3e80 65 5f 64 65 6c 5f 63 6f 73 74 20 69 73 20 6e 6f 74 20 73 70 65 63 69 66 69 65 64 20 74 68 65 6e e_del_cost.is.not.specified.then
3ea0 20 64 65 66 61 75 6c 74 20 65 64 67 65 20 64 65 6c 65 74 69 6f 6e 0a 20 20 20 20 20 20 20 20 63 .default.edge.deletion.........c
3ec0 6f 73 74 20 6f 66 20 31 20 69 73 20 75 73 65 64 2e 20 20 49 66 20 65 64 67 65 5f 69 6e 73 5f 63 ost.of.1.is.used...If.edge_ins_c
3ee0 6f 73 74 20 69 73 20 6e 6f 74 20 73 70 65 63 69 66 69 65 64 20 74 68 65 6e 0a 20 20 20 20 20 20 ost.is.not.specified.then.......
3f00 20 20 64 65 66 61 75 6c 74 20 65 64 67 65 20 69 6e 73 65 72 74 69 6f 6e 20 63 6f 73 74 20 6f 66 ..default.edge.insertion.cost.of
3f20 20 31 20 69 73 20 75 73 65 64 2e 0a 0a 20 20 20 20 75 70 70 65 72 5f 62 6f 75 6e 64 20 3a 20 6e .1.is.used.......upper_bound.:.n
3f40 75 6d 65 72 69 63 0a 20 20 20 20 20 20 20 20 4d 61 78 69 6d 75 6d 20 65 64 69 74 20 64 69 73 74 umeric.........Maximum.edit.dist
3f60 61 6e 63 65 20 74 6f 20 63 6f 6e 73 69 64 65 72 2e 0a 0a 20 20 20 20 52 65 74 75 72 6e 73 0a 20 ance.to.consider.......Returns..
3f80 20 20 20 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 65 6e 65 72 61 74 6f 72 20 6f 66 20 63 6f 6e 73 ...-------.....Generator.of.cons
3fa0 65 63 75 74 69 76 65 20 61 70 70 72 6f 78 69 6d 61 74 69 6f 6e 73 20 6f 66 20 67 72 61 70 68 20 ecutive.approximations.of.graph.
3fc0 65 64 69 74 20 64 69 73 74 61 6e 63 65 2e 0a 0a 20 20 20 20 45 78 61 6d 70 6c 65 73 0a 20 20 20 edit.distance.......Examples....
3fe0 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 3e 3e 3e 20 47 31 20 3d 20 6e 78 2e 63 79 63 6c 65 5f .--------.....>>>.G1.=.nx.cycle_
4000 67 72 61 70 68 28 36 29 0a 20 20 20 20 3e 3e 3e 20 47 32 20 3d 20 6e 78 2e 77 68 65 65 6c 5f 67 graph(6).....>>>.G2.=.nx.wheel_g
4020 72 61 70 68 28 37 29 0a 20 20 20 20 3e 3e 3e 20 66 6f 72 20 76 20 69 6e 20 6e 78 2e 6f 70 74 69 raph(7).....>>>.for.v.in.nx.opti
4040 6d 69 7a 65 5f 67 72 61 70 68 5f 65 64 69 74 5f 64 69 73 74 61 6e 63 65 28 47 31 2c 20 47 32 29 mize_graph_edit_distance(G1,.G2)
4060 3a 0a 20 20 20 20 2e 2e 2e 20 20 20 20 20 6d 69 6e 76 20 3d 20 76 0a 20 20 20 20 3e 3e 3e 20 6d :.............minv.=.v.....>>>.m
4080 69 6e 76 0a 20 20 20 20 37 2e 30 0a 0a 20 20 20 20 53 65 65 20 41 6c 73 6f 0a 20 20 20 20 2d 2d inv.....7.0......See.Also.....--
40a0 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 67 72 61 70 68 5f 65 64 69 74 5f 64 69 73 74 61 6e 63 65 2c 20 ------.....graph_edit_distance,.
40c0 6f 70 74 69 6d 69 7a 65 5f 65 64 69 74 5f 70 61 74 68 73 0a 0a 20 20 20 20 52 65 66 65 72 65 6e optimize_edit_paths......Referen
40e0 63 65 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 5a 65 ces.....----------........[1].Ze
4100 69 6e 61 20 41 62 75 2d 41 69 73 68 65 68 2c 20 52 6f 6d 61 69 6e 20 52 61 76 65 61 75 78 2c 20 ina.Abu-Aisheh,.Romain.Raveaux,.
4120 4a 65 61 6e 2d 59 76 65 73 20 52 61 6d 65 6c 2c 20 50 61 74 72 69 63 6b 0a 20 20 20 20 20 20 20 Jean-Yves.Ramel,.Patrick........
4140 4d 61 72 74 69 6e 65 61 75 2e 20 41 6e 20 45 78 61 63 74 20 47 72 61 70 68 20 45 64 69 74 20 44 Martineau..An.Exact.Graph.Edit.D
4160 69 73 74 61 6e 63 65 20 41 6c 67 6f 72 69 74 68 6d 20 66 6f 72 20 53 6f 6c 76 69 6e 67 0a 20 20 istance.Algorithm.for.Solving...
4180 20 20 20 20 20 50 61 74 74 65 72 6e 20 52 65 63 6f 67 6e 69 74 69 6f 6e 20 50 72 6f 62 6c 65 6d .....Pattern.Recognition.Problem
41a0 73 2e 20 34 74 68 20 49 6e 74 65 72 6e 61 74 69 6f 6e 61 6c 20 43 6f 6e 66 65 72 65 6e 63 65 20 s..4th.International.Conference.
41c0 6f 6e 0a 20 20 20 20 20 20 20 50 61 74 74 65 72 6e 20 52 65 63 6f 67 6e 69 74 69 6f 6e 20 41 70 on........Pattern.Recognition.Ap
41e0 70 6c 69 63 61 74 69 6f 6e 73 20 61 6e 64 20 4d 65 74 68 6f 64 73 20 32 30 31 35 2c 20 4a 61 6e plications.and.Methods.2015,.Jan
4200 20 32 30 31 35 2c 0a 20 20 20 20 20 20 20 4c 69 73 62 6f 6e 2c 20 50 6f 72 74 75 67 61 6c 2e 20 .2015,........Lisbon,.Portugal..
4220 32 30 31 35 2c 0a 20 20 20 20 20 20 20 3c 31 30 2e 35 32 32 30 2f 30 30 30 35 32 30 39 32 30 32 2015,........<10.5220/0005209202
4240 37 31 30 32 37 38 3e 2e 20 3c 68 61 6c 2d 30 31 31 36 38 38 31 36 3e 0a 20 20 20 20 20 20 20 68 710278>..<hal-01168816>........h
4260 74 74 70 73 3a 2f 2f 68 61 6c 2e 61 72 63 68 69 76 65 73 2d 6f 75 76 65 72 74 65 73 2e 66 72 2f ttps://hal.archives-ouvertes.fr/
4280 68 61 6c 2d 30 31 31 36 38 38 31 36 0a 20 20 20 20 54 4e 72 14 00 00 00 29 0d 72 0e 00 00 00 72 hal-01168816.....TNr....).r....r
42a0 0f 00 00 00 72 15 00 00 00 72 16 00 00 00 72 17 00 00 00 72 18 00 00 00 72 19 00 00 00 72 1a 00 ....r....r....r....r....r....r..
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43a0 01 00 97 00 64 01 64 02 6c 00 8a 2e 64 01 64 02 6c 01 8a 33 74 04 00 00 00 00 00 00 00 00 02 00 ....d.d.l...d.d.l..3t...........
43c0 47 00 64 03 84 00 64 04 ab 02 00 00 00 00 00 00 ab 00 00 00 00 00 00 00 8a 26 88 26 88 33 66 02 G.d...d..................&.&.3f.
43e0 64 05 84 08 8a 2b 64 06 84 00 8a 27 64 07 84 00 8a 30 64 08 84 00 8a 32 64 11 88 26 88 00 88 01 d....+d....'d....0d....2d..&....
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4440 8a 29 74 07 00 00 00 00 00 00 00 00 89 00 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .)t...........j.................
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4540 00 00 00 00 00 00 7c 0f ab 01 00 00 00 00 00 00 7d 14 89 2e 6a 13 00 00 00 00 00 00 00 00 00 00 ......|.........}...j...........
4560 00 00 00 00 00 00 00 00 7c 13 7c 14 7a 00 00 00 7c 13 7c 14 7a 00 00 00 66 02 ab 01 00 00 00 00 ........|.|.z...|.|.z...f.......
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4600 91 03 8c 27 04 00 8c 2e 04 00 63 03 7d 17 7d 16 ab 01 00 00 00 00 00 00 6a 17 00 00 00 00 00 00 ...'......c.}.}.........j.......
4620 00 00 00 00 00 00 00 00 00 00 00 00 7c 13 7c 14 ab 02 00 00 00 00 00 00 7c 15 64 01 7c 13 85 02 ............|.|.........|.d.|...
4640 64 01 7c 14 85 02 66 02 3c 00 00 00 7c 0c 72 be 02 00 7c 04 89 00 6a 08 00 00 00 00 00 00 00 00 d.|...f.<...|.r...|...j.........
4660 00 00 00 00 00 00 00 00 00 00 7f 11 19 00 00 00 89 01 6a 08 00 00 00 00 00 00 00 00 00 00 00 00 ..................j.............
4680 00 00 00 00 00 00 7f 12 19 00 00 00 ab 02 00 00 00 00 00 00 7d 10 6e 9a 7c 02 72 97 89 2e 6a 15 ....................}.n.|.r...j.
46a0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 0e 44 00 8f 16 8f 17 63 03 67 00 63 02 ..................|.D.....c.g.c.
46c0 5d 38 00 00 7d 16 7c 0f 44 00 5d 31 00 00 7d 17 64 0e 74 19 00 00 00 00 00 00 00 00 02 00 7c 02 ]8..}.|.D.]1..}.d.t...........|.
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4be0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 7c 13 7c 14 ab 02 00 00 00 00 00 00 7c 15 ..................|.|.........|.
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52e0 20 6d 69 6e 69 6d 75 6d 20 63 6f 73 74 20 6f 66 20 65 64 69 74 20 70 61 74 68 2e 0a 0a 20 20 20 .minimum.cost.of.edit.path......
5300 20 50 61 72 61 6d 65 74 65 72 73 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 47 .Parameters.....----------.....G
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5340 61 70 68 73 20 47 31 20 61 6e 64 20 47 32 20 6d 75 73 74 20 62 65 20 6f 66 20 74 68 65 20 73 61 aphs.G1.and.G2.must.be.of.the.sa
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53a0 72 6e 73 20 54 72 75 65 20 69 66 20 6e 6f 64 65 20 6e 31 20 69 6e 20 47 31 20 61 6e 64 20 6e 32 rns.True.if.node.n1.in.G1.and.n2
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5400 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 20 77 69 6c 6c 20 62 65 20 63 61 6c 6c 65 64 20 ....The.function.will.be.called.
5420 6c 69 6b 65 0a 0a 20 20 20 20 20 20 20 20 20 20 20 6e 6f 64 65 5f 6d 61 74 63 68 28 47 31 2e 6e like.............node_match(G1.n
5440 6f 64 65 73 5b 6e 31 5d 2c 20 47 32 2e 6e 6f 64 65 73 5b 6e 32 5d 29 2e 0a 0a 20 20 20 20 20 20 odes[n1],.G2.nodes[n2]).........
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54a0 64 69 63 74 69 6f 6e 61 72 69 65 73 20 66 6f 72 20 6e 31 20 61 6e 64 20 6e 32 20 61 73 20 69 6e dictionaries.for.n1.and.n2.as.in
54c0 70 75 74 73 2e 0a 0a 20 20 20 20 20 20 20 20 49 67 6e 6f 72 65 64 20 69 66 20 6e 6f 64 65 5f 73 puts...........Ignored.if.node_s
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5500 68 65 72 0a 20 20 20 20 20 20 20 20 6e 6f 64 65 5f 6d 61 74 63 68 20 6e 6f 72 20 6e 6f 64 65 5f her.........node_match.nor.node_
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55c0 64 69 63 74 69 6f 6e 61 72 69 65 73 0a 20 20 20 20 20 20 20 20 66 6f 72 20 74 68 65 20 70 61 69 dictionaries.........for.the.pai
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5640 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 20 77 69 6c 6c 20 62 65 20 63 ..........The.function.will.be.c
5660 61 6c 6c 65 64 20 6c 69 6b 65 0a 0a 20 20 20 20 20 20 20 20 20 20 20 65 64 67 65 5f 6d 61 74 63 alled.like.............edge_matc
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56a0 20 20 20 20 54 68 61 74 20 69 73 2c 20 74 68 65 20 66 75 6e 63 74 69 6f 6e 20 77 69 6c 6c 20 72 ....That.is,.the.function.will.r
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56e0 20 20 64 69 63 74 69 6f 6e 61 72 69 65 73 20 6f 66 20 74 68 65 20 65 64 67 65 73 20 75 6e 64 65 ..dictionaries.of.the.edges.unde
5700 72 20 63 6f 6e 73 69 64 65 72 61 74 69 6f 6e 2e 0a 0a 20 20 20 20 20 20 20 20 49 67 6e 6f 72 65 r.consideration...........Ignore
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5760 68 20 6e 6f 72 20 65 64 67 65 5f 73 75 62 73 74 5f 63 6f 73 74 20 61 72 65 20 73 70 65 63 69 66 h.nor.edge_subst_cost.are.specif
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57e0 6e 73 5f 63 6f 73 74 20 3a 20 63 61 6c 6c 61 62 6c 65 0a 20 20 20 20 20 20 20 20 46 75 6e 63 74 ns_cost.:.callable.........Funct
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5860 65 63 74 69 76 65 6c 79 2e 0a 0a 20 20 20 20 20 20 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e 73 ectively...........The.functions
5880 20 77 69 6c 6c 20 62 65 20 63 61 6c 6c 65 64 20 6c 69 6b 65 0a 0a 20 20 20 20 20 20 20 20 20 20 .will.be.called.like............
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58c0 32 2e 6e 6f 64 65 73 5b 6e 32 5d 29 2c 0a 20 20 20 20 20 20 20 20 20 20 20 6e 6f 64 65 5f 64 65 2.nodes[n2]),............node_de
58e0 6c 5f 63 6f 73 74 28 47 31 2e 6e 6f 64 65 73 5b 6e 31 5d 29 2c 0a 20 20 20 20 20 20 20 20 20 20 l_cost(G1.nodes[n1]),...........
5900 20 6e 6f 64 65 5f 69 6e 73 5f 63 6f 73 74 28 47 32 2e 6e 6f 64 65 73 5b 6e 32 5d 29 2e 0a 0a 20 .node_ins_cost(G2.nodes[n2])....
5920 20 20 20 20 20 20 20 54 68 61 74 20 69 73 2c 20 74 68 65 20 66 75 6e 63 74 69 6f 6e 73 20 77 69 .......That.is,.the.functions.wi
5940 6c 6c 20 72 65 63 65 69 76 65 20 74 68 65 20 6e 6f 64 65 20 61 74 74 72 69 62 75 74 65 0a 20 20 ll.receive.the.node.attribute...
5960 20 20 20 20 20 20 64 69 63 74 69 6f 6e 61 72 69 65 73 20 61 73 20 69 6e 70 75 74 73 2e 20 20 54 ......dictionaries.as.inputs...T
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59a0 75 72 6e 0a 20 20 20 20 20 20 20 20 70 6f 73 69 74 69 76 65 20 6e 75 6d 65 72 69 63 20 76 61 6c urn.........positive.numeric.val
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59e0 74 5f 63 6f 73 74 20 6f 76 65 72 72 69 64 65 73 20 6e 6f 64 65 5f 6d 61 74 63 68 20 69 66 20 73 t_cost.overrides.node_match.if.s
5a00 70 65 63 69 66 69 65 64 2e 0a 20 20 20 20 20 20 20 20 49 66 20 6e 65 69 74 68 65 72 20 6e 6f 64 pecified..........If.neither.nod
5a20 65 5f 6d 61 74 63 68 20 6e 6f 72 20 6e 6f 64 65 5f 73 75 62 73 74 5f 63 6f 73 74 20 61 72 65 20 e_match.nor.node_subst_cost.are.
5a40 73 70 65 63 69 66 69 65 64 20 74 68 65 6e 0a 20 20 20 20 20 20 20 20 64 65 66 61 75 6c 74 20 6e specified.then.........default.n
5a60 6f 64 65 20 73 75 62 73 74 69 74 75 74 69 6f 6e 20 63 6f 73 74 20 6f 66 20 30 20 69 73 20 75 73 ode.substitution.cost.of.0.is.us
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eae0 2c 20 30 29 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 ,.0)......References.....-------
eb00 2d 2d 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 5a 68 61 6e 67 2c 20 4a 2e 2c 20 54 61 6e 67 2c 20 ---........[1].Zhang,.J.,.Tang,.
eb20 4a 2e 2c 20 4d 61 2c 20 43 2e 2c 20 54 6f 6e 67 2c 20 48 2e 2c 20 4a 69 6e 67 2c 20 59 2e 2c 20 J.,.Ma,.C.,.Tong,.H.,.Jing,.Y.,.
eb40 26 20 4c 69 2c 20 4a 2e 0a 20 20 20 20 20 20 20 20 20 20 20 50 61 6e 74 68 65 72 3a 20 46 61 73 &.Li,.J.............Panther:.Fas
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eba0 65 64 69 6e 67 73 20 6f 66 20 74 68 65 20 41 43 4d 20 53 49 47 4b 44 44 20 49 6e 74 65 72 6e 61 edings.of.the.ACM.SIGKDD.Interna
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ebe0 4b 6e 6f 77 6c 65 64 67 65 20 44 69 73 63 6f 76 65 72 79 20 61 6e 64 20 44 61 74 61 20 4d 69 6e Knowledge.Discovery.and.Data.Min
ec00 69 6e 67 20 28 56 6f 6c 2e 20 32 30 31 35 2d 41 75 67 75 73 74 2c 20 70 70 2e 20 31 34 34 35 e2 ing.(Vol..2015-August,.pp..1445.
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ec40 66 6f 72 20 43 6f 6d 70 75 74 69 6e 67 20 4d 61 63 68 69 6e 65 72 79 2e 20 68 74 74 70 73 3a 2f for.Computing.Machinery..https:/
ec60 2f 64 6f 69 2e 6f 72 67 2f 31 30 2e 31 31 34 35 2f 32 37 38 33 32 35 38 2e 32 37 38 33 32 36 37 /doi.org/10.1145/2783258.2783267
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f6a0 0a 20 20 20 20 20 20 20 20 54 68 69 73 20 69 73 20 60 60 54 60 60 20 69 6e 20 5b 31 5d 5f 2e 20 .........This.is.``T``.in.[1]_..
f6c0 41 63 63 6f 72 64 69 6e 67 20 74 6f 20 74 68 65 20 70 61 70 65 72 2c 20 60 60 54 20 3e 3d 20 35 According.to.the.paper,.``T.>=.5
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fe20 20 30 2c 20 35 2c 20 30 2c 20 39 2c 20 38 5d 5d 0a 0a 20 20 20 20 52 65 66 65 72 65 6e 63 65 73 .0,.5,.0,.9,.8]]......References
fe40 0a 20 20 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 20 20 20 20 2e 2e 20 5b 31 5d 20 5a 68 61 6e 67 .....----------........[1].Zhang
fe60 2c 20 4a 2e 2c 20 54 61 6e 67 2c 20 4a 2e 2c 20 4d 61 2c 20 43 2e 2c 20 54 6f 6e 67 2c 20 48 2e ,.J.,.Tang,.J.,.Ma,.C.,.Tong,.H.
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fea0 50 61 6e 74 68 65 72 3a 20 46 61 73 74 20 74 6f 70 2d 6b 20 73 69 6d 69 6c 61 72 69 74 79 20 73 Panther:.Fast.top-k.similarity.s
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fee0 20 20 20 20 49 6e 20 50 72 6f 63 65 65 64 69 6e 67 73 20 6f 66 20 74 68 65 20 41 43 4d 20 53 49 ....In.Proceedings.of.the.ACM.SI
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