§ \ùMh‘ ãó‚—dZddlZddgZejd¬¦«d„¦«Zejd¬¦«d„¦«ZdS) z$ Utilities for connectivity package éNÚ!build_auxiliary_node_connectivityÚ!build_auxiliary_edge_connectivityT)Ú returns_graphcóR—| ¦«}i}tj¦«}t|¦«D]\\}}|||<| |›d|¬¦«| |›d|¬¦«| |›d|›dd¬¦«Œ]g}| ¦«D]Y\}}| ||›d||›df¦«|s)| ||›d||›df¦«ŒZ| |d¬¦«||j d<|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 úf/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/networkx/algorithms/connectivity/utils.pyrr s\€ð<}Š}‰Œ€Hà€GÝ Œ ‰ Œ €Aå˜Q‘<”<ð1ð1‰ˆˆ4؈‰ Ø Š a777˜tˆ Ñ$Ô$Ð$Ø Š a777˜tˆ Ñ$Ô$Ð$Ø Š a777˜q˜G˜G˜G¨aˆ Ñ0Ô0Ð0Ð0à €EØŸ'š'™)œ)ðIðI‰ˆØ Š ˜ œÐ+Ð+Ð+°¸´Ð-BÐ-BÐ-BÐCÑDÔDÐDØð IØ LŠL˜W Vœ_Ð/Ð/Ð/°G¸F´OÐ1FÐ1FÐ1FÐGÑ HÔ HÐ HøØ×ÒU QÐÑ'Ô'Ð'ð!€A„GˆIÑØ €HócóÚ—| ¦«retj¦«}| | ¦«¦«| | ¦«d¬¦«|Stj¦«}| | ¦«¦«| ¦«D]"\}}| ||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?sÕ€ð ‡}‚}„ð Ý ŒJ‰LŒLˆØ ×Ò˜Ÿš™œÑ#Ô#Ð#Ø ×Ò˜Ÿš™œ¨QÐÑ/Ô/Ð/Øˆå ŒJ‰LŒLˆØ ×Ò˜Ÿš™œÑ#Ô#Ð#ØŸgšg™iœið Oð O‰NˆFFØ × Ò ˜v vÐ.°¸Ð0@ÐAÈAÐ Ñ NÔ NÐ NÐ N؈r )Ú__doc__ÚnetworkxrÚ__all__Ú _dispatchablerr©r rúr)s‹ððððÐÐÐà .Ð0SÐ T€ð€Ô Ð%Ñ%Ô%ð1 ð1 ñ&Ô%ð1 ðh€Ô Ð%Ñ%Ô%ððñ&Ô%ðððr