edge_reciprocity

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

Calculate the edge reciprocity of the graph.

Parameters:

gGraph

Graph to be used edges.

weightEdgePropertyMap (optional, default: None)

Edge weights.

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 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...