networkx.algorithms.approximation.connectivity.local_node_connectivity¶

local_node_connectivity(G, source, target, cutoff=None)[source]

Compute node connectivity between source and target.

Pairwise or local node connectivity between two distinct and nonadjacent nodes is the minimum number of nodes that must be removed (minimum separating cutset) to disconnect them. By Menger’s theorem, this is equal to the number of node independent paths (paths that share no nodes other than source and target). Which is what we compute in this function.

This algorithm is a fast approximation that gives an strict lower bound on the actual number of node independent paths between two nodes 1. It works for both directed and undirected graphs.

Parameters
• G (NetworkX graph)

• source (node) – Starting node for node connectivity

• target (node) – Ending node for node connectivity

• cutoff (integer) – Maximum node connectivity to consider. If None, the minimum degree of source or target is used as a cutoff. Default value None.

Returns

k – pairwise node connectivity

Return type

integer

Examples

>>> # Platonic octahedral graph has node connectivity 4
>>> # for each non adjacent node pair
>>> from networkx.algorithms import approximation as approx
>>> G = nx.octahedral_graph()
>>> approx.local_node_connectivity(G, 0, 5)
4

Notes

This algorithm 1 finds node independents paths between two nodes by computing their shortest path using BFS, marking the nodes of the path found as ‘used’ and then searching other shortest paths excluding the nodes marked as used until no more paths exist. It is not exact because a shortest path could use nodes that, if the path were longer, may belong to two different node independent paths. Thus it only guarantees an strict lower bound on node connectivity.

Note that the authors propose a further refinement, losing accuracy and gaining speed, which is not implemented yet.

References

1(1,2)

White, Douglas R., and Mark Newman. 2001 A Fast Algorithm for Node-Independent Paths. Santa Fe Institute Working Paper #01-07-035 http://eclectic.ss.uci.edu/~drwhite/working.pdf