104 lines
3.0 KiB
Python
104 lines
3.0 KiB
Python
|
# -*- 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']
|
||
|
|
|
||
|
|
|
||
|
|
@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)
|
||
|
|
|
||
|
|
|
||
|
|
@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)
|