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

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 . It works for both directed and undirected graphs.

Notes

This algorithm 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.

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: integer

pairwise node connectivity

Compute node connectivity between source and target.

See Also

all_pairs_node_connectivity
node_connectivity

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
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.algorithms.approximation.connectivity.node_connectivity networkx.algorithms.approximation.connectivity.local_node_connectivity networkx.algorithms.approximation.connectivity.all_pairs_node_connectivity

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /networkx/algorithms/approximation/connectivity.py#15
type: <class 'function'>
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