efficiency

efficiency(G, u, v)

Returns the efficiency of a pair of nodes in a graph.

The efficiency of a pair of nodes is the multiplicative inverse of the shortest path distance between the nodes [1]. Returns 0 if no path between nodes.

Parameters:

Gnetworkx.Graph

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

u, vnode

Nodes in the graph G.

Returns:

float

Multiplicative inverse of the shortest path distance between the nodes.

See also

local_efficiency

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.efficiency(G, 2, 3)  # this gives efficiency for node 2 and 3
0.5

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Additional backends implement this function

graphblas : OpenMP-enabled sparse linear algebra backend.