+ )iRt^RIHt^RIHt^RIHt^RIt^RI H t ^RI H t ] t R.t] !R4]PRR l44tR tR tR tR tR#)z, Moody and White algorithm for k-components ) defaultdict) combinations) itemgetterN) edmonds_karp)not_implemented_for k_componentsdirectedc \\4pVf\p\P!V4F8p\ V4p\ V4^8gK V^,PV4K: \P!V4Uu.uFqPPV4NK ppVF8p\ V4p\ V4^8gK V^,PV4K: VEFFp \ V 4^8:dK\P!WR7p V ^8d!W*,P\ V 44\\P!WVR74p V \WV 43.p V 'gKV R,wr\V4pV PV4p\P!VVR7pVV 8d)V^8d"VV,P\ V44\\P!VVVR74p V 'd!V PV\VV V434KK \!V4#uupi \dT P4Ki;i)a/ Returns the k-component structure of a graph G. A `k`-component is a maximal subgraph of a graph G that has, at least, node connectivity `k`: we need to remove at least `k` nodes to break it into more components. `k`-components have an inherent hierarchical structure because they are nested in terms of connectivity: a connected graph can contain several 2-components, each of which can contain one or more 3-components, and so forth. Parameters ---------- G : NetworkX graph flow_func : function Function to perform the underlying flow computations. Default value :meth:`edmonds_karp`. This function performs better in sparse graphs with right tailed degree distributions. :meth:`shortest_augmenting_path` will perform better in denser graphs. Returns ------- k_components : dict Dictionary with all connectivity levels `k` in the input Graph as keys and a list of sets of nodes that form a k-component of level `k` as values. Raises ------ NetworkXNotImplemented If the input graph is directed. Examples -------- >>> # Petersen graph has 10 nodes and it is triconnected, thus all >>> # nodes are in a single component on all three connectivity levels >>> G = nx.petersen_graph() >>> k_components = nx.k_components(G) Notes ----- Moody and White [1]_ (appendix A) provide an algorithm for identifying k-components in a graph, which is based on Kanevsky's algorithm [2]_ for finding all minimum-size node cut-sets of a graph (implemented in :meth:`all_node_cuts` function): 1. Compute node connectivity, k, of the input graph G. 2. Identify all k-cutsets at the current level of connectivity using Kanevsky's algorithm. 3. Generate new graph components based on the removal of these cutsets. Nodes in a cutset belong to both sides of the induced cut. 4. If the graph is neither complete nor trivial, return to 1; else end. This implementation also uses some heuristics (see [3]_ for details) to speed up the computation. See also -------- node_connectivity all_node_cuts biconnected_components : special case of this function when k=2 k_edge_components : similar to this function, but uses edge-connectivity instead of node-connectivity References ---------- .. [1] Moody, J. and D. White (2003). Social cohesion and embeddedness: A hierarchical conception of social groups. American Sociological Review 68(1), 103--28. http://www2.asanet.org/journals/ASRFeb03MoodyWhite.pdf .. [2] Kanevsky, A. (1993). Finding all minimum-size separating vertex sets in a graph. Networks 23(6), 533--541. http://onlinelibrary.wiley.com/doi/10.1002/net.3230230604/abstract .. [3] Torrents, J. and F. Ferraro (2015). Structural Cohesion: Visualization and Heuristics for Fast Computation. https://arxiv.org/pdf/1503.04476v1 ) flow_func)kr )rlistdefault_flow_funcnxconnected_componentssetlenappendbiconnected_componentssubgraphnode_connectivity all_node_cuts_generate_partitionnext StopIterationpop_reconstruct_k_components)Gr r componentcompc bicomponents bicomponentbicompBr cutsstackparent_k partitionnodesCthis_ks&& j/var/www/html/photoedit/myenv/lib/python3.14/site-packages/networkx/algorithms/connectivity/kcomponents.pyrrstt$L% ,,Q/ 9~ t9q= O " "4 ( 0 ,.+D+DQ+GH+GaJJqM+GLH# [! v;? O " "6 * $  q6Q;    8 q5 O " "3q6 *B$$QyAB(!456e$)"I !X YJJu%--a9EH$! (//A7B,,Q&INOLL&*=av*N!OP%< %\ 22II4!   sH59B+H::IIc#paa"\P!4p\\V44oVP S4VP VV3Rl\ S^444\P!V4F0p\P!VUu.uF pSV,NK up!xK2 R#uupi5i)aWMerge sets that share k or more elements. See: http://rosettacode.org/wiki/Set_consolidation The iterative python implementation posted there is faster than this because of the overhead of building a Graph and calling nx.connected_components, but it's not clear for us if we can use it in NetworkX because there is no licence for the code. c3|<"TF1wr\SV,SV,,4S8gK,W3xK3 R#5iN)r).0uvr r)s& r, _consolidate..s5141SqE!H9L5MQR5R1s)< <N) rGraphdict enumerateadd_nodes_fromadd_edges_fromrrrunion)setsr rrnr)s&f @r, _consolidater=s  A 4 !EU'q1,,Q/ iiI6Iq%((I67706sBB6B1 $B6c #6"Rp.pVUUu0uF qUFqfkK K pppVP4UUu0uFwrhW8gK VkK uppV, p VPV 4p \\\P !V 44F\p YUu0uFqc!WV 4'gKVkK up,p \ V 4VP48gKKVPV 4K^ \WB^,4RjxL R#uuppiuuppiuupiL5i)ca\;QJd%V3RlW,4F 'gK R# R#!V3RlW,44#)c3,<"TF qS9xK R#5ir/)r0r<r(s& r,r3E_generate_partition..has_nbrs_in_partition..s37a >7TF)any)rnoder(s&&fr,has_nbrs_in_partition2_generate_partition..has_nbrs_in_partitions0s3173ss3s3s317333N) degreermaprrrrorderrr=) rr%r rF componentscutr< n_in_cutsdr)Hccrs &&& r,rrs4J"0dsCqCdI088: /:41QQ: /) ;E 5A#r..q12YRY2Gb2Q!!YRR y>AGGI %   i (3JA...1 /S/sE DDD D D  ADD&D,$D*D?DDca/pV'd \V4M^p\V^R4EFpW28Xd \\W,V44W&K)W09d'\\W^,,V44W&KU\P !W,!oW^,,Uu.uFGp\ ;QJdV3RlV4F 'gK RM RM!V3RlV44'gKEVNKI ppV'd'\\W,V,V44W&K\\W,V44W&EK V#uupi)c3,<"TF qS9xK R#5ir/rA)r0r< nodes_at_ks& r,r3,_reconstruct_k_components..s5USTaz6ISTrCTFr )maxranger r=rr:rD)k_compsresultmax_kr r to_addrUs& @r,rrs F#CLE 5!R  :\'*a89FI  \&Q-;rmsl$"2.   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