global_efficiency#

global_efficiency(G)[source]#

Returns the average global 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 average global efficiency of a graph is the average efficiency of all pairs of nodes [1].

Parameters:

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

Returns:

float: The average global efficiency of the graph.

See also

local_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)])
>>> round(nx.global_efficiency(G), 12)
0.916666666667