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