# Source code for networkx.algorithms.reciprocity

```
# -*- coding: utf-8 -*-
# Copyright (C) 2015-2019 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
#
# Authors: Haochen Wu (wuhaochen42@gmail.com)
"""Algorithms to calculate reciprocity in a directed graph."""
from networkx import NetworkXError
from ..utils import not_implemented_for
__all__ = ['reciprocity', 'overall_reciprocity']
[docs]@not_implemented_for('undirected', 'multigraph')
def reciprocity(G, nodes=None):
r"""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
----------
G : graph
A networkx directed graph
nodes : container of nodes, optional (default=whole graph)
Compute reciprocity for nodes in this container.
Returns
-------
out : dictionary
Reciprocity keyed by node label.
Notes
-----
The reciprocity is not defined for isolated nodes.
In such cases this function will return None.
"""
# If `nodes` is not specified, calculate the reciprocity of the graph.
if nodes is None:
return overall_reciprocity(G)
# If `nodes` represents a single node in the graph, return only its
# reciprocity.
if nodes in G:
reciprocity = next(_reciprocity_iter(G, nodes))[1]
if reciprocity is None:
raise NetworkXError('Not defined for isolated nodes.')
else:
return reciprocity
# Otherwise, `nodes` represents an iterable of nodes, so return a
# dictionary mapping node to its reciprocity.
return dict(_reciprocity_iter(G, nodes))
def _reciprocity_iter(G, nodes):
""" Return an iterator of (node, reciprocity).
"""
n = G.nbunch_iter(nodes)
for node in n:
pred = set(G.predecessors(node))
succ = set(G.successors(node))
overlap = pred & succ
n_total = len(pred) + len(succ)
# Reciprocity is not defined for isolated nodes.
# Return None.
if n_total == 0:
yield (node, None)
else:
reciprocity = 2.0 * float(len(overlap)) / float(n_total)
yield (node, reciprocity)
[docs]@not_implemented_for('undirected', 'multigraph')
def overall_reciprocity(G):
"""Compute the reciprocity for the whole graph.
See the doc of reciprocity for the definition.
Parameters
----------
G : graph
A networkx graph
"""
n_all_edge = G.number_of_edges()
n_overlap_edge = (n_all_edge - G.to_undirected().number_of_edges()) * 2
if n_all_edge == 0:
raise NetworkXError("Not defined for empty graphs")
return float(n_overlap_edge) / float(n_all_edge)
```