average_node_connectivity¶

average_node_connectivity(G, flow_func=None)[source]¶

Returns the average connectivity of a graph G.

The average connectivity \(\bar{\kappa}\) of a graph G is the average of local node connectivity over all pairs of nodes of G [R215] .

\[\bar{\kappa}(G) = \frac{\sum_{u,v} \kappa_{G}(u,v)}{{n \choose 2}}\]

Parameters:

G : NetworkX graph Undirected graph flow_func : function 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 local_node_connectivity() for details. The choice of the default function may change from version to version and should not be relied on. Default value: None.

Returns:

K : float Average node connectivity

See also

local_node_connectivity(), node_connectivity(), edge_connectivity(), maximum_flow(), edmonds_karp(), preflow_push(), shortest_augmenting_path()

References

[R215]

(1, 2) Beineke, L., O. Oellermann, and R. Pippert (2002). The average connectivity of a graph. Discrete mathematics 252(1-3), 31-45. http://www.sciencedirect.com/science/article/pii/S0012365X01001807