є ,╡[c@sFdZddlZdjdgГZddgZdДZdДZdS( s$ Utilities for connectivity package i Ns s%Jordi Torrents t!build_auxiliary_node_connectivityt!build_auxiliary_edge_connectivityc Cs'|jГ}i}tjГ}xpt|ГD]b\}}|||<|jd|d|Г|jd|d|Г|jd|d|ddГq+Wg}xi|jГD][\}}|jd||d||fГ|sд|jd||d||fГqдqдW|j|ddГ||j d<|S( sUCreates 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. http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf s%dAtids%dBtcapacityis%sBs%sAtmapping( tis_directedtnxtDiGrapht enumeratetadd_nodetadd_edgetedgestappendtadd_edges_fromtgraph( tGtdirectedRtHtitnodeRtsourcettarget((sElib/python2.7/site-packages/networkx/algorithms/connectivity/utils.pyR s "#* cCs▒|jГrHtjГ}|j|jГГ|j|jГddГ|StjГ}|j|jГГx?|jГD]1\}}|j||f||fgddГqtW|SdS(sRAuxiliary 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 RiN(RRRtadd_nodes_fromtnodesR R(RRRR((sElib/python2.7/site-packages/networkx/algorithms/connectivity/utils.pyRAs)(t__doc__tnetworkxRtjoint __author__t__all__RR(((sElib/python2.7/site-packages/networkx/algorithms/connectivity/utils.pyts 4