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 andm
edges we derive a directed graph D with2n
nodes and2m+n
arcs by replacing each original nodev
with two nodesvA
,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 andm
arcs we derive a directed graph D with2n
nodes andm+n
arcs by replacing each original nodev
with two nodesvA
,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[â€˜mappingâ€™].
References
[1]Kammer, Frank and Hanjo Taubig. Graph Connectivity. in Brandes and Erlebach, â€˜Network Analysis: Methodological Foundationsâ€™, Lecture Notes in Computer Science, Volume 3418, Springer-Verlag, 2005. https://doi.org/10.1007/978-3-540-31955-9_7