Ë ·¯wg‘ ãó|—dZddlZddgZejd¬«d„«Zejd¬«d„«Zy) z$ Utilities for connectivity package éNÚ!build_auxiliary_node_connectivityÚ!build_auxiliary_edge_connectivityT)Ú returns_graphcó—|j«}i}tj«}t|«D]P\}}|||<|j |›d|¬«|j |›d|¬«|j |›d|›dd¬«ŒRg}|j «D]F\}}|j||›d||›df«|rŒ(|j||›d||›df«ŒH|j|d¬«||jd<|S)a/Creates 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 ÚA)ÚidÚBé©ÚcapacityÚmapping) Ú is_directedÚnxÚDiGraphÚ enumerateÚadd_nodeÚadd_edgeÚedgesÚappendÚadd_edges_fromÚgraph) ÚGÚdirectedr ÚHÚiÚnoderÚsourceÚtargets úk/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/algorithms/connectivity/utils.pyrr s*€ð<}‰}‹€Hà€GÜ ‰ ‹ €Aä˜Q“<ò1‰ˆˆ4؈‰ Ø ‰ aS˜7˜tˆ Ô$Ø ‰ aS˜7˜tˆ Ô$Ø ‰ aS˜7˜q˜c ˜G¨aˆ Õ0ð 1ð €EØŸ'™'›)òI‰ˆØ ‰ ˜ ™Ð)¨Ð+°¸±Ð/@ÀÐ-BÐCÔDÚØ L‰L˜W V™_Ð-¨QÐ/°G¸F±OÐ3DÀAÐ1FÐGÕ HðIð×ÑU QÐÔ'ð!€A‡GGˆIÑØ €Hócóš—|j«rVtj«}|j|j ««|j |j «d¬«|Stj«}|j|j ««|j «D]\}}|j ||f||fgd¬«Œ |S)aRAuxiliary 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 )rrrÚadd_nodes_fromÚnodesrr)rrrrs rrr?s«€ð ‡}}„Ü J‰J‹LˆØ ×јŸ™›Ô#Ø ×јŸ™›¨QÐÔ/؈ä J‰J‹LˆØ ×јŸ™›Ô#ØŸg™g›iò O‰NˆFFØ × Ñ ˜v vÐ.°¸Ð0@ÐAÈAÐ Õ Nð Oàˆr )Ú__doc__ÚnetworkxrÚ__all__Ú _dispatchablerr©r rúr)s]ðñóà .Ð0SÐ T€ð€×Ñ Ô%ñ1 ó&ð1 ðh€×Ñ Ô%ñó&ñr