D^(hExdZddlZddlZgdZej dgdZej dgdZejddd d d i dd Z ejddd d d i ddZ ejddd d d i ddZ dZ ddZ dZdZdZdZdZdZdZdZdZy)uu *************** VF2++ Algorithm *************** An implementation of the VF2++ algorithm [1]_ for Graph Isomorphism testing. The simplest interface to use this module is to call: `vf2pp_is_isomorphic`: to check whether two graphs are isomorphic. `vf2pp_isomorphism`: to obtain the node mapping between two graphs, in case they are isomorphic. `vf2pp_all_isomorphisms`: to generate all possible mappings between two graphs, if isomorphic. Introduction ------------ The VF2++ algorithm, follows a similar logic to that of VF2, while also introducing new easy-to-check cutting rules and determining the optimal access order of nodes. It is also implemented in a non-recursive manner, which saves both time and space, when compared to its previous counterpart. The optimal node ordering is obtained after taking into consideration both the degree but also the label rarity of each node. This way we place the nodes that are more likely to match, first in the order, thus examining the most promising branches in the beginning. The rules also consider node labels, making it easier to prune unfruitful branches early in the process. Examples -------- Suppose G1 and G2 are Isomorphic Graphs. Verification is as follows: Without node labels: >>> import networkx as nx >>> G1 = nx.path_graph(4) >>> G2 = nx.path_graph(4) >>> nx.vf2pp_is_isomorphic(G1, G2, node_label=None) True >>> nx.vf2pp_isomorphism(G1, G2, node_label=None) {1: 1, 2: 2, 0: 0, 3: 3} With node labels: >>> G1 = nx.path_graph(4) >>> G2 = nx.path_graph(4) >>> mapped = {1: 1, 2: 2, 3: 3, 0: 0} >>> nx.set_node_attributes( ... G1, dict(zip(G1, ["blue", "red", "green", "yellow"])), "label" ... ) >>> nx.set_node_attributes( ... G2, ... dict(zip([mapped[u] for u in G1], ["blue", "red", "green", "yellow"])), ... "label", ... ) >>> nx.vf2pp_is_isomorphic(G1, G2, node_label="label") True >>> nx.vf2pp_isomorphism(G1, G2, node_label="label") {1: 1, 2: 2, 0: 0, 3: 3} References ---------- .. [1] Jüttner, Alpár & Madarasi, Péter. (2018). "VF2++—An improved subgraph isomorphism algorithm". Discrete Applied Mathematics. 242. https://doi.org/10.1016/j.dam.2018.02.018 N)vf2pp_isomorphismvf2pp_is_isomorphicvf2pp_all_isomorphisms_GraphParameters)G1G2 G1_labels G2_labelsnodes_of_G1Labelsnodes_of_G2LabelsG2_nodes_of_degree_StateParameters) mappingreverse_mappingT1T1_inT1_tilde T1_tilde_inT2T2_inT2_tilde T2_tilde_in)rr node_label default_label)graphs node_attrscT tt||||}|S#t$rYywxYw)aReturn an isomorphic mapping between `G1` and `G2` if it exists. Parameters ---------- G1, G2 : NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is `None`, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is `None`. Returns ------- dict or None Node mapping if the two graphs are isomorphic. None otherwise. N)nextr StopIteration)rrrrrs c/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/networkx/algorithms/isomorphism/vf2pp.pyrrks40-b"j-PQ s  ''c"t||||yy)aExamines whether G1 and G2 are isomorphic. Parameters ---------- G1, G2 : NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is `None`, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is `None`. Returns ------- bool True if the two graphs are isomorphic, False otherwise. TF)r)rrrrs r!rrs0R];G c #K|jdk(s|jdk(ry|jrt|j|jDcic]\\}}\}}|||f}}}}}t|j|jDcic]\\}}\}}|||f} }}}}n*t |j }t |j } |js t} t} n t} t} |j|jk7ryt|jt| jk7ryt||| ||\} } t| syt!| }g}t#| |d| | |}|j%|d|f| j&}| j(}d}|r|d\}} t+|}t1||| | rt3||jdz k(r|j5}|||<|]|||<|||<t7||| | t#| ||| | |}|j%|||f|dz }|ryycc}}}}wcc}}}}w#t,$rU|j/|dz}|r:|d\}}||}|j/||j/|| ||| | YwxYww)aYields all the possible mappings between G1 and G2. Parameters ---------- G1, G2 : NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is `None`, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is `None`. Yields ------ dict Isomorphic mapping between the nodes in `G1` and `G2`. rFrN)number_of_nodes is_directedzip in_degree out_degreedictdegree_find_candidates_restore_Tinout_find_candidates_Di_restore_Tinout_Diordersortedvalues_initialize_parameters_precheck_label_properties_matching_orderiterappendrrrr pop _feasibilitylencopy_update_Tinout)rrrrnr)_r* G1_degree G2_degreefind_candidatesrestore_Tinout graph_params state_params node_orderstack candidatesrr matching_node current_nodecandidate_nodes candidate popped_node1 popped_node2 cp_mappings r!rrs0 q B$6$6$8A$= ~~47r||R]]3S  /IJ  :& &  47r||R]]3S  /IJ  :& &  O O >> *(-+ xxzRXXZ i !VI,<,<,>%??"8 B :}"L, &l 3!.J E 1 |\9MJ LL*Q-,-""G"22OM (-b % o _-I  i| L7|r113a77$\\^ +4 <(  %.GL !)5OI & <L, O}-|\9J LL*]3Z@ A Q MK e  f  IIK Q M"') a&|4  L)##L1|\<V  sKAK1J 4*K1J 3D+K1 J*BK1>K1AK.*K1-K..K1c`|\}}}}}}tfd|jDryy)Nc3dK|]'\}}|vxst|t|k7)ywN)r;).0labelnodesr s r! z-_precheck_label_properties.. s?  E5 &&U#.?.F*G3u:*UU s-0FT)anyitems)rDrrr r r r?r s @r!r5r5s?LXIBIy"35F  -335  r#c t|j||}t|j||}t||||tjj |tjj |tjj |}t t } }t t } } |jrGt |jt } } t |jt }}nFt |jt } } t |jt }}tii|| | | | | || }||fS)a6Initializes all the necessary parameters for VF2++ Parameters ---------- G1,G2: NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism or monomorphism G1_labels,G2_labels: dict The label of every node in G1 and G2 respectively Returns ------- graph_params: namedtuple Contains all the Graph-related parameters: G1,G2 G1_labels,G2_labels: dict state_params: namedtuple Contains all the State-related parameters: mapping: dict The mapping as extended so far. Maps nodes of G1 to nodes of G2 reverse_mapping: dict The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed T1, T2: set Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are neighbors of nodes that are. T1_out, T2_out: set Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti )datadefault) r+rUrnxutilsgroupssetr'r)rrrArrr r rDrrrrrrrrrEs r!r4r4(s.FRXX:}XEFIRXX:}XEFI#    "  "  "LsuBsuB ~~  O E!$BHHJ+ #BHHJ+ #BHHJ+#       L  %%r#c|\}}}}}s|siSjrjdtj}|j Dcic]\}}|t |c}}Dcic]}|dc}g}|rUt fd|D} |D cgc]} | | k(s| } } t| j} tj| D]} | j}|stfd|D}|D cgc] } | |k(s | }} tfd|D}|D cgc]} j| |k(s| }} t |fd}|j|j|D]}|xxd z cc<|j||xxd zcc<|j||r܌|rU|Scc}}wcc}wcc} wcc} wcc} w) a{The node ordering as introduced in VF2++. Notes ----- Taking into account the structure of the Graph and the node labeling, the nodes are placed in an order such that, most of the unfruitful/infeasible branches of the search space can be pruned on high levels, significantly decreasing the number of visited states. The premise is that, the algorithm will be able to recognize inconsistencies early, proceeding to go deep into the search tree only if it's needed. Parameters ---------- graph_params: namedtuple Contains: G1,G2: NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism or monomorphism. G1_labels,G2_labels: dict The label of every node in G1 and G2 respectively. Returns ------- node_order: list The ordering of the nodes. T)as_viewrc3.K|] }|ywrR)rSxr label_raritys r!rVz"_matching_order..sJil3Js)keyc3(K|] }| ywrRrc)rSr> used_degreess r!rVz"_matching_order..s%L!l1o%Lsc3<K|]}j|ywrR)r,)rSr>rs r!rVz"_matching_order..s M!1 Msc|SrRrc)rdr res r!z!_matching_order..sL14Nr#r)r' to_undirectedr_rUrXr;minmaxr,r\ bfs_layersr<r8 neighborsremovediscard)rDrr?r V1_unorderedrTrUnoderF max_rarityr> rarest_nodesmax_node dlevel_nodes nodes_to_addmax_used_degreemax_used_degree_nodes max_degreemax_degree_nodes next_noderr rerhs @@@@r!r6r6ts%45A1BIq!. b  ~~   d  +rxxz?L:K:Q:Q:ST,%E3u:%TL(*+D!G+LJ J\JJ # |IaL'AZ'OA  |3MM"h7 0L',,.L"%%L|%L"L+)|A//QA)%)! M7L MM 4$ ! 8RA$ $ $*N !!),LL3,D &!+&,##I.Yy12a72$$Y/' 0 < EU+  )$s0#G* G0,G5=G5 G:,G: G?"G?c X|\}}}}}}} |\ } } }}}}}}} }||D cgc] } | | vs|  }} |st|||}|j| |||j| |j| |jrD|j|Dchc])}|j |||j ||k7r|+c}|S|d}t|| |}|ddD]}|j|| ||j| |j| |||j||||jrD|j|Dchc])}|j |||j ||k7r|+c}|Scc} wcc}wcc}w)aGiven node u of G1, finds the candidates of u from G2. Parameters ---------- u: Graph node The node from G1 for which to find the candidates from G2. graph_params: namedtuple Contains all the Graph-related parameters: G1,G2: NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism or monomorphism G1_labels,G2_labels: dict The label of every node in G1 and G2 respectively state_params: namedtuple Contains all the State-related parameters: mapping: dict The mapping as extended so far. Maps nodes of G1 to nodes of G2 reverse_mapping: dict The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed T1, T2: set Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are neighbors of nodes that are. T1_tilde, T2_tilde: set Ti_tilde contains all the nodes from Gi, that are neither in the mapping nor in Ti Returns ------- candidates: set The nodes from G2 which are candidates for u. rrN)r_intersection_updatedifference_update is_multigraphnumber_of_edges)urDrEr@rrr r?r r rrrnbr covered_nbrsrHrtnbr1 common_nodess r!r-r-sPFRBBIq!.0B>J;G_aAq!Q!#%a5;CC7NC;L; *9Q<89 &&'9)A,'GH&&x0$$_5     ( (!+))!Q/23E3EdD3QQ  ?Dr'$-()LQR <((GDM):;<""?3$$%7 ! %EF$$%6y|%DE &&) %%a+r/A/A$/MM   C<& s FF.F"&.F'c T|\}}}}}}} |\ } } }}}}}}} }||D cgc] } | | vs|  }} |j|Dcgc] }|| vs| }}|s|st|||}|j| |||j| |j| |j rD|j|Dchc])}|j |||j ||k7r|+c}|S|rL|d}t|j| |}|ddD]#}|j|j| |%n!|j }t|| |}|D]}|j|| ||j| |j| |||j||||j rD|j|Dchc])}|j |||j ||k7r|+c}|Scc} wcc}wcc}wcc}w)Nrr)predr_rrrrr9)rrDrEr@rrr r?r r rrrsucccovered_successorsrcovered_predecessorsrHrtsucc1rpred1s r!r/r/ slEQBBIq!.0B>J;G_aAq!Q!+-a5D4DGO$DD-/WWQZKT47?DKK "6*9Q<89 &&'9)A,'GH&&x0$$_5     ( (!+))!Q/23E3EdD3QQ "1%27775>23 '+ FE  , ,RWWWU^-D E F%((*2gen-. %=((GEN);<=""?3$$%7 ! %EF$$%6y|%DE &&) %%a+r/A/A$/MM   UEK4 s" HH H H=.H .H%cx|j}t||||ry|jrt||||syy)aGiven a candidate pair of nodes u and v from G1 and G2 respectively, checks if it's feasible to extend the mapping, i.e. if u and v can be matched. Notes ----- This function performs all the necessary checking by applying both consistency and cutting rules. Parameters ---------- node1, node2: Graph node The candidate pair of nodes being checked for matching graph_params: namedtuple Contains all the Graph-related parameters: G1,G2: NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism or monomorphism G1_labels,G2_labels: dict The label of every node in G1 and G2 respectively state_params: namedtuple Contains all the State-related parameters: mapping: dict The mapping as extended so far. Maps nodes of G1 to nodes of G2 reverse_mapping: dict The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed T1, T2: set Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are neighbors of nodes that are. T1_out, T2_out: set Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti Returns ------- True if all checks are successful, False otherwise. FT)r_cut_PTr_consistent_PT)node1node2rDrErs r!r:r:;s?T Bue\<8 eUL,G r#c |\}}}}}|\ }}}}} }} } } }ii}} jrtjjjDcic]}||| c}} tjjjDcic]}||| c}}t | j t |j k7rytjjDcic]}||| c}}tjjDcic]}||| c}}t |j t |j k7ry|jD]\}}||}jrHtfd|D}tfd|D}tdt||Dryt|j|t| j|k7ryt| j|t| j|k7ryjst|j|t| j|k7syjsy| jD]\}}||}jrHtfd|D}tfd|D}tdt||Dryt|j|t| j|k7ryt| j|t| j|k7ryt|j|t| j|k7s yycc}wcc}wcc}wcc}w) aImplements the cutting rules for the ISO problem. Parameters ---------- u, v: Graph node The two candidate nodes being examined. graph_params: namedtuple Contains all the Graph-related parameters: G1,G2: NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism or monomorphism G1_labels,G2_labels: dict The label of every node in G1 and G2 respectively state_params: namedtuple Contains all the State-related parameters: mapping: dict The mapping as extended so far. Maps nodes of G1 to nodes of G2 reverse_mapping: dict The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed T1, T2: set Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are neighbors of nodes that are. T1_tilde, T2_tilde: set Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti Returns ------- True if we should prune this branch, i.e. the node pair failed the cutting checks. False otherwise. Tc3BK|]}j|ywrRrrSrdrrs r!rVz_cut_PT..!Kq""4"4Q":!Kc3BK|]}j|ywrRrrSrdrvs r!rVz_cut_PT..rrc3,K|] \}}||k7ywrRrcrS u_nbr_edges v_nbr_edgess r!rVz_cut_PT..!,K{*Fc3BK|]}j|ywrRrrs r!rVz_cut_PT..!Lq""4"4Q":!Lrc3BK|]}j|ywrRrrs r!rVz_cut_PT..rrc3,K|] \}}||k7ywrRrcrs r!rVz_cut_PT..rr)r'r\r]r^rr_keysrXrr2rWr(r; intersection)rrrDrEr r r?rrrrrru_labels_predecessorsv_labels_predecessorsn1n2u_labels_successorsv_labels_successorsrTG1_nbhG2_nbh u_nbrs_edges v_nbrs_edgesG1_predG2_pred u_pred_edges v_pred_edgesrrs`` @@r!rrqsJ-9)BIy!Q          46r0 ~~ ")+ 42R2  4! !#)+ 42R2  4!  $))+ ,4I4N4N4P0Q Q((//r!u*M2y}+<*MN((//r!u*M2y}+<*MN  # # %&#.A.F.F.H*II,224 v$U+   !!KF!KKL!!KF!KKL03L,0O rv& '3rv/F+G G x$$V, -X5J5J65R1S S >> E$6$6v$> ?3   v &D ! ), >> /557w'.   !!LG!LLL!!LG!LLL03L,0O rw' (C0H,I I x$$W- .#h6K6KG6T2U U u!!'* +s53E3Eg3N/O O%( { 5 5 +N*Ms O O O!4 O&cv|j|j}}|j|j}}||D]1}||vs|j |||j |||k7s1y||D]1}||vs|j ||||j ||k7s1y|j sy|j |D]1} | |vs|j | ||j || |k7s1y|j |D]1} | |vs|j || ||j | |k7s1yy)aChecks the consistency of extending the mapping using the current node pair. Parameters ---------- u, v: Graph node The two candidate nodes being examined. graph_params: namedtuple Contains all the Graph-related parameters: G1,G2: NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism or monomorphism G1_labels,G2_labels: dict The label of every node in G1 and G2 respectively state_params: namedtuple Contains all the State-related parameters: mapping: dict The mapping as extended so far. Maps nodes of G1 to nodes of G2 reverse_mapping: dict The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed T1, T2: set Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are neighbors of nodes that are. T1_out, T2_out: set Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti Returns ------- True if the pair passes all the consistency checks successfully. False otherwise. FT)rrrrrr'r) rrrDrErrrrneighbor predecessors r!rrs}J__looB+33\5Q5Q_GqE w !!!X."2D2D78$3 qE  &!!!_X%>?2CUCU8D  >> wwqz ' !!!+q1R5G5G $a6 wwqz / )!! ,a##K34  r#c ||\}}}}}}}|\ }}} } } } } }}}||Dchc] }||vs| }}||Dchc] }||vs| }}| j|| j|| j|| j|| j||j|| j||j||jsy|j|Dchc] }||vs| }}|j|Dchc] }||vs| }}| j||j|| j||j|| j||j|| j||j|ycc}wcc}wcc}wcc}w)aKUpdates the Ti/Ti_out (i=1,2) when a new node pair u-v is added to the mapping. Notes ----- This function should be called right after the feasibility checks are passed, and node1 is mapped to node2. The purpose of this function is to avoid brute force computing of Ti/Ti_out by iterating over all nodes of the graph and checking which nodes satisfy the necessary conditions. Instead, in every step of the algorithm we focus exclusively on the two nodes that are being added to the mapping, incrementally updating Ti/Ti_out. Parameters ---------- new_node1, new_node2: Graph node The two new nodes, added to the mapping. graph_params: namedtuple Contains all the Graph-related parameters: G1,G2: NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism or monomorphism G1_labels,G2_labels: dict The label of every node in G1 and G2 respectively state_params: namedtuple Contains all the State-related parameters: mapping: dict The mapping as extended so far. Maps nodes of G1 to nodes of G2 reverse_mapping: dict The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed T1, T2: set Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are neighbors of nodes that are. T1_tilde, T2_tilde: set Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti N)updaterrrr'r) new_node1 new_node2rDrErrr?rrrrrrrrrrruncovered_successors_G1uncovered_successors_G2runcovered_predecessors_G1uncovered_predecessors_G2s r!r=r=1sP)BAq!Q      139 UWATtUUI$o*E II%&II%&JJyJJy 67 67 Y Y >> +!t7/B!!+!t?/J!! LL*+ LL*+ MM) MM) 89 89 Y YEV$!!s- F*F* F/F/0 F4:F4 F9F9c |\}}}}}}}|\ }}} } } } } }d}||D]T}|vrd}|j|tfd||Dr3|j|| j|V|s| j|d}||D]T}|vrd}| j|tfd||Dr3| j|| j|V|s| j|yy)aRestores the previous version of Ti/Ti_out when a node pair is deleted from the mapping. Parameters ---------- popped_node1, popped_node2: Graph node The two nodes deleted from the mapping. graph_params: namedtuple Contains all the Graph-related parameters: G1,G2: NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism or monomorphism G1_labels,G2_labels: dict The label of every node in G1 and G2 respectively state_params: namedtuple Contains all the State-related parameters: mapping: dict The mapping as extended so far. Maps nodes of G1 to nodes of G2 reverse_mapping: dict The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed T1, T2: set Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are neighbors of nodes that are. T1_tilde, T2_tilde: set Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti FTc3&K|]}|v ywrRrc)rSrrs r!rVz"_restore_Tinout..s:c3'>:c3&K|]}|v ywrRrc)rSrrs r!rVz"_restore_Tinout..sBc3/)BrN)addrWrr)rMrNrDrErrr?rrrrrrrris_addedrrrs @@r!r.r.s+D)BAq!Q      H|$ # w H FF< :R\:: JJx LL " #  \"H|$#  &H FF< BR\BB JJx LL "#  \" r#c l|\}}}}}}}|\ }}} } } } } }d}||D]}|vrd}|j|tfd|j|Ds|j|tfd||Ds|j|||vsz||vs| j||j|D]}|vrd}|j|tfd|j|Ds|j|tfd||Ds|j|||vrz||vr| j||s| j|d}||D]}|vrd}| j|tfd|j|Ds| j|tfd||Ds| j||| vsz|| vs| j||j|D]}|vrd}| j|tfd |j|Ds| j|tfd ||Ds| j||| vrz|| vr| j||s| j|yy) NFTc3&K|]}|v ywrRrcrSrrs r!rVz%_restore_Tinout_Di..sF4twFrc3&K|]}|v ywrRrcrSrrs r!rVz%_restore_Tinout_Di..sA4twArc3&K|]}|v ywrRrcrs r!rVz%_restore_Tinout_Di..sH4twHrc3&K|]}|v ywrRrcrs r!rVz%_restore_Tinout_Di..sC4twCrc3&K|]}|v ywrRrcrSrrs r!rVz%_restore_Tinout_Di..sN4t.Nrc3&K|]}|v ywrRrcrSrrs r!rVz%_restore_Tinout_Di..sI4t.Irc3&K|]}|v ywrRrcrs r!rVz%_restore_Tinout_Di..)sP4t.Prc3&K|]}|v ywrRrcrs r!rVz%_restore_Tinout_Di..,sK4t.Kr)rrWrrr)rMrNrDrErrr?rrrrrrrrr successorrrrs @@r!r0r0s(BAq!Q      H %,  H IIl #F27793EFF 9%A2i=AA i("E)LL+,"ww|,* ' !H FF< H277;3GHH ;'C2k?CC k*2%)= [)*"  \"H % ,  'H IIl #N2779;MNN 9%I2i=II i("E)LL+ ,ww|,* / )H FF< P277;;OPP ;'K2k?KK k*2%)= [)*  \" r#)NN)Nr%)__doc__ collectionsnetworkxr\__all__ namedtuplerr _dispatchablerrrr5r4r6r-r/r:rrr=r.r0rcr#r!rs&DL P);)) *;)) "+8WXY<+8WXY8+8WXsYslI&XDNL^.b3lslGTX vM#`W#r#