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Source code for networkx.algorithms.wiener

# wiener.py - functions related to the Wiener index of a graph
# Copyright 2015 NetworkX developers.
# This file is part of NetworkX.
# NetworkX is distributed under a BSD license; see LICENSE.txt for more
# information.
"""Functions related to the Wiener index of a graph."""
from __future__ import division

from itertools import chain

from .components import is_connected
from .components import is_strongly_connected
from .shortest_paths import shortest_path_length as spl

__all__ = ['wiener_index']

#: Rename the :func:`chain.from_iterable` function for the sake of
#: brevity.
chaini = chain.from_iterable

[docs]def wiener_index(G, weight=None): """Returns the Wiener index of the given graph. The *Wiener index* of a graph is the sum of the shortest-path distances between each pair of reachable nodes. For pairs of nodes in undirected graphs, only one orientation of the pair is counted. Parameters ---------- G : NetworkX graph weight : object The edge attribute to use as distance when computing shortest-path distances. This is passed directly to the :func:`networkx.shortest_path_length` function. Returns ------- float The Wiener index of the graph `G`. Raises ------ NetworkXError If the graph `G` is not connected. Notes ----- If a pair of nodes is not reachable, the distance is assumed to be infinity. This means that for graphs that are not strongly-connected, this function returns ``inf``. The Wiener index is not usually defined for directed graphs, however this function uses the natural generalization of the Wiener index to directed graphs. Examples -------- The Wiener index of the (unweighted) complete graph on *n* nodes equals the number of pairs of the *n* nodes, since each pair of nodes is at distance one:: >>> import networkx as nx >>> n = 10 >>> G = nx.complete_graph(n) >>> nx.wiener_index(G) == n * (n - 1) / 2 True Graphs that are not strongly-connected have infinite Wiener index:: >>> G = nx.empty_graph(2) >>> nx.wiener_index(G) inf """ is_directed = G.is_directed() if (is_directed and not is_strongly_connected(G)) or \ (not is_directed and not is_connected(G)): return float('inf') total = sum(chaini(p.values() for v, p in spl(G, weight=weight))) # Need to account for double counting pairs of nodes in undirected graphs. return total if is_directed else total / 2