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# Source code for networkx.algorithms.wiener

# wiener.py - functions related to the Wiener index of a graph
#
#
# This file is part of NetworkX.
#
# 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.