networkx.algorithms.connectivity.utils.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 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