h pSrSSKrSS/r\R"SS9S5r\R"SS9S5rg) z$ Utilities for connectivity package N!build_auxiliary_node_connectivity!build_auxiliary_edge_connectivityT) returns_graphcUR5n0n[R"5n[U5HFupEXBU'UR US3US9 UR US3US9 UR US3US3SS9 MH /nUR 5HHupxURX'S3X(S345 U(aM+URX(S3X'S345 MJ URUSS9 X#RS'U$)aCreates a directed graph D from an undirected graph G to compute flow based node connectivity. For an undirected graph G having `n` nodes and `m` edges we derive a directed graph D with `2n` nodes and `2m+n` arcs by replacing each original node `v` with two nodes `vA`, `vB` linked by an (internal) arc in D. Then for each edge (`u`, `v`) in G we add two arcs (`uB`, `vA`) and (`vB`, `uA`) in D. Finally we set the attribute capacity = 1 for each arc in D [1]_. For a directed graph having `n` nodes and `m` arcs we derive a directed graph D with `2n` nodes and `m+n` arcs by replacing each original node `v` with two nodes `vA`, `vB` linked by an (internal) arc (`vA`, `vB`) in D. Then for each arc (`u`, `v`) in G we add one arc (`uB`, `vA`) in D. Finally we set the attribute capacity = 1 for each arc in D. A dictionary with a mapping between nodes in the original graph and the auxiliary digraph is stored as a graph attribute: D.graph['mapping']. References ---------- .. [1] Kammer, Frank and Hanjo Taubig. Graph Connectivity. in Brandes and Erlebach, 'Network Analysis: Methodological Foundations', Lecture Notes in Computer Science, Volume 3418, Springer-Verlag, 2005. https://doi.org/10.1007/978-3-540-31955-9_7 A)idBcapacitymapping) is_directednxDiGraph enumerateadd_nodeadd_edgeedgesappendadd_edges_fromgraph) Gdirectedr Hinodersourcetargets ^/var/www/html/shao/venv/lib/python3.13/site-packages/networkx/algorithms/connectivity/utils.pyrr s<}}HG AQ<  aS7t $ aS7t $ aS7qcGa 0  E'') )+/@-BCDx LLW_-Q/GO3DA1FG H$UQ'!GGI HcUR5(aT[R"5nURUR 55 UR UR 5SS9 U$[R"5nURUR 55 UR 5Hup#UR X#4X24/SS9 M U$)a*Auxiliary digraph for computing flow based edge connectivity If the input graph is undirected, we replace each edge (`u`,`v`) with two reciprocal arcs (`u`, `v`) and (`v`, `u`) and then we set the attribute 'capacity' for each arc to 1. If the input graph is directed we simply add the 'capacity' attribute. Part of algorithm 1 in [1]_ . References ---------- .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms. (this is a chapter, look for the reference of the book). http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf r r )rrradd_nodes_fromnodesrr)rrrrs rrr?s }} JJL # Q/ JJL #ggiNF  v.0@AA  N(r )__doc__networkxr__all__ _dispatchablerrr rr)sY .0S T%1 &1 h%&r