node_connectivity(G, s=None, t=None, flow_func=None)
Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial. If source and target nodes are provided, this function returns the local node connectivity: the minimum number of nodes that must be removed to break all paths from source to target in G.
This is a flow based implementation of node connectivity. The algorithm works by solving $O((n-\delta-1+\delta(\delta-1)/2))$ maximum flow problems on an auxiliary digraph. Where $\delta$ is the minimum degree of G. For details about the auxiliary digraph and the computation of local node connectivity see local_node_connectivity
. This implementation is based on algorithm 11 in .
Undirected graph
Source node. Optional. Default value: None.
Target node. Optional. Default value: None.
A function for computing the maximum flow among a pair of nodes. The function has to accept at least three parameters: a Digraph, a source node, and a target node. And return a residual network that follows NetworkX conventions (see maximum_flow
for details). If flow_func is None, the default maximum flow function ( edmonds_karp
) is used. See below for details. The choice of the default function may change from version to version and should not be relied on. Default value: None.
Node connectivity of G, or local node connectivity if source and target are provided.
Returns node connectivity for a graph or digraph G.
edge_connectivity
meth
edmonds_karp
meth
maximum_flow
meth
preflow_push
meth
>>> # Platonic icosahedral graph is 5-node-connected
... G = nx.icosahedral_graph()
... nx.node_connectivity(G) 5
You can use alternative flow algorithms for the underlying maximum flow computation. In dense networks the algorithm shortest_augmenting_path
will usually perform better than the default edmonds_karp
, which is faster for sparse networks with highly skewed degree distributions. Alternative flow functions have to be explicitly imported from the flow package.
>>> from networkx.algorithms.flow import shortest_augmenting_path
... nx.node_connectivity(G, flow_func=shortest_augmenting_path) 5
If you specify a pair of nodes (source and target) as parameters, this function returns the value of local node connectivity.
>>> nx.node_connectivity(G, 3, 7) 5
If you need to perform several local computations among different pairs of nodes on the same graph, it is recommended that you reuse the data structures used in the maximum flow computations. See local_node_connectivity
for details.
The following pages refer to to this document either explicitly or contain code examples using this.
networkx.algorithms.connectivity.connectivity.edge_connectivity
networkx.algorithms.connectivity.kcutsets.all_node_cuts
networkx.algorithms.connectivity.connectivity.local_node_connectivity
networkx.algorithms.connectivity.connectivity.average_node_connectivity
networkx.algorithms.connectivity.connectivity.local_edge_connectivity
networkx.algorithms.connectivity.connectivity.node_connectivity
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