ʏkh |dZddlZddgZejddZejddZy) z$ Utilities for connectivity package N!build_auxiliary_node_connectivity!build_auxiliary_edge_connectivityT) returns_graphc|j}i}tj}t|D]P\}}|||<|j |d||j |d||j |d|ddRg}|j D]F\}}|j||d||df|r(|j||d||dfH|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 A)idBcapacitymapping) is_directednxDiGraph enumerateadd_nodeadd_edgeedgesappendadd_edges_fromgraph) Gdirectedr Hinodersourcetargets b/var/www/teggl/fontify/venv/lib/python3.12/site-packages/networkx/algorithms/connectivity/utils.pyrr s*<}}HG AQ<14  aS7t $ aS7t $ aS7qcGa 0 1 E'')I )+/@-BCD LLWV_-Q/GFO3DA1FG HIUQ'!AGGI Hc|jrVtj}|j|j |j |j d|Stj}|j|j |j D]\}}|j ||f||fgd |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 )rrradd_nodes_fromnodesrr)rrrrs rrr?s }} JJL # Q/ JJL #ggi ONFF  vv.0@AA  N Or )__doc__networkxr__all__ _dispatchablerrr rr)s] .0S T%1 &1 h%&r