ó ,µ[c @sdZddlmZddlZddlZddlTddlZdZdddd gZ d „Z e e e e e e e e e d „ Z e e e e e e e e e d „ Z e e e e e e e e e d „ Ze e e e e e e e e ed„ Zd„ZdS(sP Functions measuring similarity using graph edit distance. The graph edit distance is the number of edge/node changes needed to make two graphs isomorphic. The default algorithm/implementation is sub-optimal for some graphs. The problem of finding the exact Graph Edit Distance (GED) is NP-hard so it is often slow. If the simple interface `graph_edit_distance` takes too long for your graph, try `optimize_graph_edit_distance` and/or `optimize_edit_paths`. At the same time, I encourage capable people to investigate alternative GED algorithms, in order to improve the choices available. iÿÿÿÿ(tprint_functionN(t*s%Andrey Paramonov tgraph_edit_distancetoptimal_edit_pathstoptimize_graph_edit_distancetoptimize_edit_pathscOst||ŽdS(N(tprint(targstkwargs((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pyt debug_print(sc  CsQd} xDt|||||||||| | tƒ D]\} } }|} q4W| S(sÙReturns GED (graph edit distance) between graphs G1 and G2. Graph edit distance is a graph similarity measure analogous to Levenshtein distance for strings. It is defined as minimum cost of edit path (sequence of node and edge edit operations) transforming graph G1 to graph isomorphic to G2. Parameters ---------- G1, G2: graphs The two graphs G1 and G2 must be of the same type. node_match : callable A function that returns True if node n1 in G1 and n2 in G2 should be considered equal during matching. The function will be called like node_match(G1.nodes[n1], G2.nodes[n2]). That is, the function will receive the node attribute dictionaries for n1 and n2 as inputs. Ignored if node_subst_cost is specified. If neither node_match nor node_subst_cost are specified then node attributes are not considered. edge_match : callable A function that returns True if the edge attribute dictionaries for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be considered equal during matching. The function will be called like edge_match(G1[u1][v1], G2[u2][v2]). That is, the function will receive the edge attribute dictionaries of the edges under consideration. Ignored if edge_subst_cost is specified. If neither edge_match nor edge_subst_cost are specified then edge attributes are not considered. node_subst_cost, node_del_cost, node_ins_cost : callable Functions that return the costs of node substitution, node deletion, and node insertion, respectively. The functions will be called like node_subst_cost(G1.nodes[n1], G2.nodes[n2]), node_del_cost(G1.nodes[n1]), node_ins_cost(G2.nodes[n2]). That is, the functions will receive the node attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function node_subst_cost overrides node_match if specified. If neither node_match nor node_subst_cost are specified then default node substitution cost of 0 is used (node attributes are not considered during matching). If node_del_cost is not specified then default node deletion cost of 1 is used. If node_ins_cost is not specified then default node insertion cost of 1 is used. edge_subst_cost, edge_del_cost, edge_ins_cost : callable Functions that return the costs of edge substitution, edge deletion, and edge insertion, respectively. The functions will be called like edge_subst_cost(G1[u1][v1], G2[u2][v2]), edge_del_cost(G1[u1][v1]), edge_ins_cost(G2[u2][v2]). That is, the functions will receive the edge attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function edge_subst_cost overrides edge_match if specified. If neither edge_match nor edge_subst_cost are specified then default edge substitution cost of 0 is used (edge attributes are not considered during matching). If edge_del_cost is not specified then default edge deletion cost of 1 is used. If edge_ins_cost is not specified then default edge insertion cost of 1 is used. upper_bound : numeric Maximum edit distance to consider. Return None if no edit distance under or equal to upper_bound exists. Examples -------- >>> G1 = nx.cycle_graph(6) >>> G2 = nx.wheel_graph(7) >>> nx.graph_edit_distance(G1, G2) 7.0 See Also -------- optimal_edit_paths, optimize_graph_edit_distance, is_isomorphic (test for graph edit distance of 0) References ---------- .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick Martineau. An Exact Graph Edit Distance Algorithm for Solving Pattern Recognition Problems. 4th International Conference on Pattern Recognition Applications and Methods 2015, Jan 2015, Lisbon, Portugal. 2015, <10.5220/0005209202710278>. https://hal.archives-ouvertes.fr/hal-01168816 N(tNoneRtTrue(tG1tG2t node_matcht edge_matchtnode_subst_costt node_del_costt node_ins_costtedge_subst_costt edge_del_costt edge_ins_costt upper_boundtbestcostt vertex_patht edge_pathtcost((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pyR,s{   c  Cs—tƒ} d} x{t|||||||||| | tƒ D]L\} }}| dk rp|| krptƒ} n| j| |fƒ|} q=W| | fS(sRReturns all minimum-cost edit paths transforming G1 to G2. Graph edit path is a sequence of node and edge edit operations transforming graph G1 to graph isomorphic to G2. Edit operations include substitutions, deletions, and insertions. Parameters ---------- G1, G2: graphs The two graphs G1 and G2 must be of the same type. node_match : callable A function that returns True if node n1 in G1 and n2 in G2 should be considered equal during matching. The function will be called like node_match(G1.nodes[n1], G2.nodes[n2]). That is, the function will receive the node attribute dictionaries for n1 and n2 as inputs. Ignored if node_subst_cost is specified. If neither node_match nor node_subst_cost are specified then node attributes are not considered. edge_match : callable A function that returns True if the edge attribute dictionaries for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be considered equal during matching. The function will be called like edge_match(G1[u1][v1], G2[u2][v2]). That is, the function will receive the edge attribute dictionaries of the edges under consideration. Ignored if edge_subst_cost is specified. If neither edge_match nor edge_subst_cost are specified then edge attributes are not considered. node_subst_cost, node_del_cost, node_ins_cost : callable Functions that return the costs of node substitution, node deletion, and node insertion, respectively. The functions will be called like node_subst_cost(G1.nodes[n1], G2.nodes[n2]), node_del_cost(G1.nodes[n1]), node_ins_cost(G2.nodes[n2]). That is, the functions will receive the node attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function node_subst_cost overrides node_match if specified. If neither node_match nor node_subst_cost are specified then default node substitution cost of 0 is used (node attributes are not considered during matching). If node_del_cost is not specified then default node deletion cost of 1 is used. If node_ins_cost is not specified then default node insertion cost of 1 is used. edge_subst_cost, edge_del_cost, edge_ins_cost : callable Functions that return the costs of edge substitution, edge deletion, and edge insertion, respectively. The functions will be called like edge_subst_cost(G1[u1][v1], G2[u2][v2]), edge_del_cost(G1[u1][v1]), edge_ins_cost(G2[u2][v2]). That is, the functions will receive the edge attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function edge_subst_cost overrides edge_match if specified. If neither edge_match nor edge_subst_cost are specified then default edge substitution cost of 0 is used (edge attributes are not considered during matching). If edge_del_cost is not specified then default edge deletion cost of 1 is used. If edge_ins_cost is not specified then default edge insertion cost of 1 is used. upper_bound : numeric Maximum edit distance to consider. Returns ------- edit_paths : list of tuples (node_edit_path, edge_edit_path) node_edit_path : list of tuples (u, v) edge_edit_path : list of tuples ((u1, v1), (u2, v2)) cost : numeric Optimal edit path cost (graph edit distance). Examples -------- >>> G1 = nx.cycle_graph(6) >>> G2 = nx.wheel_graph(7) >>> paths, cost = nx.optimal_edit_paths(G1, G2) >>> len(paths) 84 >>> cost 7.0 See Also -------- graph_edit_distance, optimize_edit_paths References ---------- .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick Martineau. An Exact Graph Edit Distance Algorithm for Solving Pattern Recognition Problems. 4th International Conference on Pattern Recognition Applications and Methods 2015, Jan 2015, Lisbon, Portugal. 2015, <10.5220/0005209202710278>. https://hal.archives-ouvertes.fr/hal-01168816 N(tlistR RtFalsetappend(R R RRRRRRRRRtpathsRRRR((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pyR²sƒ     c  csJxCt|||||||||| | tƒ D]\} } } | Vq.WdS(sýReturns consecutive approximations of GED (graph edit distance) between graphs G1 and G2. Graph edit distance is a graph similarity measure analogous to Levenshtein distance for strings. It is defined as minimum cost of edit path (sequence of node and edge edit operations) transforming graph G1 to graph isomorphic to G2. Parameters ---------- G1, G2: graphs The two graphs G1 and G2 must be of the same type. node_match : callable A function that returns True if node n1 in G1 and n2 in G2 should be considered equal during matching. The function will be called like node_match(G1.nodes[n1], G2.nodes[n2]). That is, the function will receive the node attribute dictionaries for n1 and n2 as inputs. Ignored if node_subst_cost is specified. If neither node_match nor node_subst_cost are specified then node attributes are not considered. edge_match : callable A function that returns True if the edge attribute dictionaries for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be considered equal during matching. The function will be called like edge_match(G1[u1][v1], G2[u2][v2]). That is, the function will receive the edge attribute dictionaries of the edges under consideration. Ignored if edge_subst_cost is specified. If neither edge_match nor edge_subst_cost are specified then edge attributes are not considered. node_subst_cost, node_del_cost, node_ins_cost : callable Functions that return the costs of node substitution, node deletion, and node insertion, respectively. The functions will be called like node_subst_cost(G1.nodes[n1], G2.nodes[n2]), node_del_cost(G1.nodes[n1]), node_ins_cost(G2.nodes[n2]). That is, the functions will receive the node attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function node_subst_cost overrides node_match if specified. If neither node_match nor node_subst_cost are specified then default node substitution cost of 0 is used (node attributes are not considered during matching). If node_del_cost is not specified then default node deletion cost of 1 is used. If node_ins_cost is not specified then default node insertion cost of 1 is used. edge_subst_cost, edge_del_cost, edge_ins_cost : callable Functions that return the costs of edge substitution, edge deletion, and edge insertion, respectively. The functions will be called like edge_subst_cost(G1[u1][v1], G2[u2][v2]), edge_del_cost(G1[u1][v1]), edge_ins_cost(G2[u2][v2]). That is, the functions will receive the edge attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function edge_subst_cost overrides edge_match if specified. If neither edge_match nor edge_subst_cost are specified then default edge substitution cost of 0 is used (edge attributes are not considered during matching). If edge_del_cost is not specified then default edge deletion cost of 1 is used. If edge_ins_cost is not specified then default edge insertion cost of 1 is used. upper_bound : numeric Maximum edit distance to consider. Returns ------- Generator of consecutive approximations of graph edit distance. Examples -------- >>> G1 = nx.cycle_graph(6) >>> G2 = nx.wheel_graph(7) >>> for v in nx.optimize_graph_edit_distance(G1, G2): ... minv = v >>> minv 7.0 See Also -------- graph_edit_distance, optimize_edit_paths References ---------- .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick Martineau. An Exact Graph Edit Distance Algorithm for Solving Pattern Recognition Problems. 4th International Conference on Pattern Recognition Applications and Methods 2015, Jan 2015, Lisbon, Portugal. 2015, <10.5220/0005209202710278>. https://hal.archives-ouvertes.fr/hal-01168816 N(RR (R R RRRRRRRRRRRR((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pyRDs ~  c  #sUddl‰ ddlm‰ ddd„ƒY‰‡‡ fd†‰ d„‰d„‰d „‰g‡‡‡‡‡‡ ‡ fd †‰ ‡ ‡fd †‰‡‡ ‡ ‡‡‡‡fd †‰‡‡‡ ‡fd †‰tˆjƒ} tˆjƒ} t| ƒ}t| ƒ}ˆ j||||fƒ}|rˆ jg| D]0}| D]#}|ˆj|ˆj|ƒ^q;q1ƒj||ƒ|d|…d|…f. https://hal.archives-ouvertes.fr/hal-01168816 iÿÿÿÿN(tlinear_sum_assignmentt CostMatrixcBseZd„ZRS(cSs(||_||_||_||_dS(N(tCt lsa_row_indt lsa_col_indtls(tselfR!R"R#R$((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pyt__init__Ns   (t__name__t __module__R&(((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pyR MscsÓˆ|ƒ\}}ttt|ƒƒ||ƒ}t‡‡fd†|Dƒƒ}ttt|ƒƒ||ƒ}t‡‡fd†|Dƒƒ}||ˆ||<||ˆ||<ˆ||||||fjƒƒS(Nc3s6|],\}}}|ˆkr|ˆkr|VqdS(N((t.0tktitj(tmtn(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys csc3s6|],\}}}|ˆkr|ˆkr|VqdS(N((R)R*R+R,(R-R.(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys es(tziptrangetlenRtsum(R!R-R.R"R#tindexest subst_indt dummy_ind(R R(R-R.s=lib/python2.7/site-packages/networkx/algorithms/similarity.pytmake_CostMatrixZs cSs–gt||ƒD]"}||kp0|||k^q}gt||ƒD]"}||kpi|||k^qJ}||dd…fdd…|fS(N(R0(R!R+R,R-R.R*trow_indtcol_ind((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pyt extract_Cms99cSs–gt||ƒD]"}||ko0|||k^q}gt||ƒD]"}||koi|||k^qJ}||dd…fdd…|fS(N(R0(R!R+R,R-R.R*R7R8((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pytreduce_Css99cSsT|g|D]}||k^q }x*t|ƒD]}|||kcd8v, u=None or v=None for deletion/insertion Returns: list of (i, j): indices of edge mappings g<->h localCe: local CostMatrix of edge mappings (basically submatrix of Ce at cross of rows i, cols j) ic3s;|]1\}}ˆˆd |ˆfˆ|ffkVqdS(iN((R)tptq(R+t pending_gtu(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys –sc3s;|]1\}}ˆˆd |ˆfˆ|ffkVqdS(iN((R)R?R@(R,t pending_htv(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys ™sc3s]|]S\}}ˆ|ˆfkr3ˆ|ˆfkpTˆˆ|fkoTˆˆ|fkVqdS(N((R)R?R@(tgthRBRD(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys ©sc3sQ|]G\}}ˆ|ˆfˆ|ffkoHˆ|ˆfˆ|ffkVqdS(N((R)R?R@(RERFRBRD(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys ®sc3su|]k\}}|ˆks'|ˆkr|ˆkr=ˆ|n ˆˆ||ˆkr^ˆ|n ˆˆ|fVqdS(N((R)R*tl(tMtNtg_indth_indR-R.(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys ¸s i(ii( R1R0tanyR!R/tnxt is_directedRR"R#tempty( RBRDRARCtCet matched_uvR!R*RGtlocalCetij(R R R R9tinfR6tnp(RHRIRERJRFRKR+R,R-R.RARCRBRDs=lib/python2.7/site-packages/networkx/algorithms/similarity.pyt match_edges€sD  --   ""   cs‹t|ƒrƒt|Œ\}}ˆt‡fd†|Dƒƒ}ˆt‡fd†|Dƒƒ}ˆˆ|j||ˆˆƒ||ƒS|SdS(Nc3s!|]}|ˆkrdVqdS(iN((R)tt(R-(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys Æsc3s!|]}|ˆkrdVqdS(iN((R)RW(R.(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys Çs(R1R/R2R!(RPRSR-R.R+R,tm_itn_j(R6R:(R-R.s=lib/python2.7/site-packages/networkx/algorithms/similarity.pyt reduce_CeÃs    %c 3sît|ƒ‰t|ƒ‰t‡‡fd†t|j|jƒDƒƒ\}} ˆ|ˆkre||nd| ˆkr~|| nd||||ƒ\} } ˆ || t|ƒt|ƒƒ} ˆ||j| j| jƒrÞnžˆˆ|j|f| fˆˆƒˆ |j|ˆ| fƒˆ |j| ˆ|fƒ|j|j|| fƒ} || f| | | |j|| f| jfVtƒ}|| ‰‰ˆˆkrLJ‡‡fd†t ˆˆƒDƒ}n&‡‡‡fd†t ˆˆƒDƒ}xÕ|D]Í\}} ˆ||j|| f|jƒr*qônˆˆ|j|f| fˆˆƒ|ˆkraˆdnˆ| ˆkrzˆdnˆƒ} ˆ||j|| f| j|jƒr´qônˆ|ˆkrÍ||nd| ˆkræ|| nd||||ƒ\} } ˆ||j|| f| j| jƒr2qônˆ || t|ƒt|ƒƒ} ˆ||j|| f| j| j| jƒr‹qôn|j || f| | | |j|| f| jfƒqôWx"t |dd„ƒD] }|VqÛWdS(sê Parameters: matched_uv: partial vertex edit path list of tuples (u, v) of vertex mappings u<->v, u=None or v=None for deletion/insertion pending_u, pending_v: lists of vertices not yet mapped Cv: CostMatrix of pending vertex mappings pending_g, pending_h: lists of edges not yet mapped Ce: CostMatrix of pending edge mappings matched_cost: cost of partial edit path Returns: sequence of (i, j): indices of vertex mapping u<->v Cv_ij: reduced CostMatrix of pending vertex mappings (basically Cv with row i, col j removed) list of (x, y): indices of edge mappings g<->h Ce_xy: reduced CostMatrix of pending edge mappings (basically Ce with rows x, cols y removed) cost: total cost of edit operation NOTE: most promising ops first c3s9|]/\}}|ˆks'|ˆkr||fVqdS(N((R)R*RG(R-R.(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys és c3sC|]9}|ˆkr|ˆks1|ˆˆkr|ˆfVqdS(N((R)RW(tfixed_itfixed_jR-(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys þsc3sC|]9}|ˆkr|ˆks1|ˆˆkrˆ|fVqdS(N((R)RW(R[R\R.(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys sitkeycSs|d|dj|djS(Niii(R$(RW((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pytsN( R1tminR/R"R#R R$R!RR0Rtsorted(RQt pending_ut pending_vtCvRARCRPt matched_costR+R,txyRRtCe_xytCv_ijtothert candidatesRW(R R6RVtpruneR:RZR>(R[R\R-R.s=lib/python2.7/site-packages/networkx/algorithms/similarity.pyt get_edit_opsÌsN  4!!!.   )&$!++!% :c  3sDˆ||j|jƒrdStt|ƒt|ƒƒs_tˆj|ƒˆ_|||fVnáˆ||||ˆˆ||ƒ} x½| D]µ\} } } } }| \}}ˆ||| j| jƒrÌq‡n|t|ƒkrí|j|ƒnd}|t|ƒkr|j|ƒnd}|j||fƒxk| D]c\}}tˆƒ}tˆƒ}|j||krtˆ|nd||krˆ|ndfƒq4Wtt d„| Dƒƒƒ}tt d„| Dƒƒƒ}t‡fd†t |ƒDƒƒ}t‡fd†t |ƒDƒƒ}x5ˆ|||| |ˆˆ| ||ƒ D] }|Vq@W|dk rn|j ||ƒn|dk r|j ||ƒn|jƒxBt |t |ƒƒD]+\}}|dk r­ˆj ||ƒq­q­WxBt |t |ƒƒD]+\}}|dk ròˆj ||ƒqòqòWx| D]}|jƒq(Wq‡WdS(s› Parameters: matched_uv: partial vertex edit path list of tuples (u, v) of vertex mappings u<->v, u=None or v=None for deletion/insertion pending_u, pending_v: lists of vertices not yet mapped Cv: CostMatrix of pending vertex mappings matched_gh: partial edge edit path list of tuples (g, h) of edge mappings g<->h, g=None or h=None for deletion/insertion pending_g, pending_h: lists of edges not yet mapped Ce: CostMatrix of pending edge mappings matched_cost: cost of partial edit path Returns: sequence of (vertex_path, edge_path, cost) vertex_path: complete vertex edit path list of tuples (u, v) of vertex mappings u<->v, u=None or v=None for deletion/insertion edge_path: complete edge edit path list of tuples (g, h) of edge mappings g<->h, g=None or h=None for deletion/insertion cost: total cost of edit path NOTE: path costs are non-increasing Ncss|]\}}|VqdS(N((R)txty((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys cscss|]\}}|VqdS(N((R)RlRm((s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys dsc3s6|],}|tˆƒkr*ˆj|ƒndVqdS(N(R1tpopR (R)Rl(RA(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys esc3s6|],}|tˆƒkr*ˆj|ƒndVqdS(N(R1RnR (R)Rm(RC(s=lib/python2.7/site-packages/networkx/algorithms/similarity.pys gs( R$tmaxR1R_tvalueRnR RRR`treversedtinsertR/(RQRaRbRct matched_ghRARCRPRdtedit_opsRSRgReRft 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