local_efficiency#

local_efficiency(G)[source]#

Returns the average local efficiency of the graph.

The efficiency of a pair of nodes in a graph is the multiplicative inverse of the shortest path distance between the nodes. The local efficiency of a node in the graph is the average global efficiency of the subgraph induced by the neighbors of the node. The average local efficiency is the average of the local efficiencies of each node [1].

Parameters:

Gnetworkx.Graph: An undirected graph for which to compute the average local efficiency.

Returns:

float: The average local efficiency of the graph.

See also

global_efficiency

Notes

Edge weights are ignored when computing the shortest path distances.

References

[1]

Latora, Vito, and Massimo Marchiori. “Efficient behavior of small-world networks.” Physical Review Letters 87.19 (2001): 198701. <https://doi.org/10.1103/PhysRevLett.87.198701>

Examples

>>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
>>> nx.local_efficiency(G)
0.9166666666666667