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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)