U ª9%eD ã@s(dZddlZddgZdd„Zdd„ZdS)z$ Utilities for connectivity package éNÚ!build_auxiliary_node_connectivityÚ!build_auxiliary_edge_connectivityc Csì| ¡}i}t ¡}t|ƒD]T\}}|||<|j|›d|d|j|›d|d|j|›d|›dddqg}| ¡D]P\}}| ||›d||›df¡|s~| ||›d||›df¡q~|j|dd||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: H.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_nodeZadd_edgeÚedgesÚappendÚadd_edges_fromÚgraph) ÚGZdirectedr ÚHÚiÚnoderÚsourceÚtarget©rúe/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/networkx/algorithms/connectivity/utils.pyr s "$ cCs~| ¡r4t ¡}| | ¡¡|j| ¡dd|St ¡}| | ¡¡| ¡D]"\}}|j||f||fgddqR|SdS)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 rrN)r r r Zadd_nodes_fromZnodesrr)rrrrrrrr=s)Ú__doc__Znetworkxr Ú__all__rrrrrrÚs4