# 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
```