edge_reciprocity

graph_tool.topology.edge_reciprocity(g, weight=None, self_loops=False)

Calculate the edge reciprocity of the graph.

Parameters:

gGraph

Graph to be used edges.

weightEdgePropertyMap (optional, default: None)

Edge weights.

self_loopsbool (optional, default: False)

Whether self-loops should be considered.

Returns:

reciprocityfloat

The reciprocity value.

Notes

The edge [reciprocity] is defined as \(E^\leftrightarrow/E\), where \(E^\leftrightarrow\) and \(E\) are the number of bidirectional and all edges in the graph, respectively. If self_loops is False, self-loops are not considered in these counds.

If weights are provided, the number of edges is replaced by the sum of edge weights.

The algorithm runs with complexity \(O(E + V)\).

Parallel implementation.

If enabled during compilation, this algorithm will run in parallel using OpenMP. See the parallel algorithms section for information about how to control several aspects of parallelization.

References

[reciprocity]

S. Wasserman and K. Faust, “Social Network Analysis”. (Cambridge University Press, Cambridge, 1994)

[lopez-reciprocity-2007]

Gorka Zamora-López, Vinko Zlatić, Changsong Zhou, Hrvoje Štefančić, and Jürgen Kurths “Reciprocity of networks with degree correlations and arbitrary degree sequences”, Phys. Rev. E 77, 016106 (2008) DOI: 10.1103/PhysRevE.77.016106 [sci-hub, @tor], arXiv: 0706.3372

Examples

>>> g = gt.Graph()
>>> g.add_vertex(2)
<...>
>>> g.add_edge(g.vertex(0), g.vertex(1))
<...>
>>> gt.edge_reciprocity(g)
0.0
>>> g.add_edge(g.vertex(1), g.vertex(0))
<...>
>>> gt.edge_reciprocity(g)
1.0
>>> g = gt.collection.data["pgp-strong-2009"]
>>> gt.edge_reciprocity(g)
0.692196963163...