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# build_auxiliary_node_connectivity¶

build_auxiliary_node_connectivity(G)[source]

Creates a directed graph D from an undirected graph G to compute flow based node connectivity.

For an undirected graph G having nodes and edges we derive a directed graph D with nodes and arcs by replacing each original node with two nodes , linked by an (internal) arc in D. Then for each edge (, ) in G we add two arcs (, ) and (, ) in D. Finally we set the attribute capacity = 1 for each arc in D [1].

For a directed graph having nodes and arcs we derive a directed graph D with nodes and arcs by replacing each original node with two nodes , linked by an (internal) arc (, ) in D. Then for each arc (, ) in G we add one arc (, ) 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