# reciprocity#

reciprocity(G, nodes=None)[source]#

Compute the reciprocity in a directed graph.

The reciprocity of a directed graph is defined as the ratio of the number of edges pointing in both directions to the total number of edges in the graph. Formally, $$r = |{(u,v) \in G|(v,u) \in G}| / |{(u,v) \in G}|$$.

The reciprocity of a single node u is defined similarly, it is the ratio of the number of edges in both directions to the total number of edges attached to node u.

Parameters:
Ggraph

A networkx directed graph

nodescontainer of nodes, optional (default=whole graph)

Compute reciprocity for nodes in this container.

Returns:
outdictionary

Reciprocity keyed by node label.

Notes

The reciprocity is not defined for isolated nodes. In such cases this function will return None.