Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Source code for networkx.algorithms.vitality

#   Aric Hagberg (hagberg@lanl.gov)
#   Renato Fabbri
#   Aric Hagberg <hagberg@lanl.gov>
#   Dan Schult <dschult@colgate.edu>
#   Pieter Swart <swart@lanl.gov>
# Copyright (C) 2016-2019 by NetworkX developers.
#
[docs]def closeness_vitality(G, node=None, weight=None, wiener_index=None): """Returns the closeness vitality for nodes in the graph. The *closeness vitality* of a node, defined in Section 3.6.2 of [1], is the change in the sum of distances between all node pairs when excluding that node. Parameters ---------- G : NetworkX graph A strongly-connected graph. weight : string The name of the edge attribute used as weight. This is passed directly to the :func:~networkx.wiener_index function. node : object If specified, only the closeness vitality for this node will be returned. Otherwise, a dictionary mapping each node to its closeness vitality will be returned. Other parameters ---------------- wiener_index : number If you have already computed the Wiener index of the graph G, you can provide that value here. Otherwise, it will be computed for you. Returns ------- dictionary or float If node is None, this function returns a dictionary with nodes as keys and closeness vitality as the value. Otherwise, it returns only the closeness vitality for the specified node. The closeness vitality of a node may be negative infinity if removing that node would disconnect the graph. Examples -------- >>> G = nx.cycle_graph(3) >>> nx.closeness_vitality(G) {0: 2.0, 1: 2.0, 2: 2.0} See Also -------- closeness_centrality References ---------- .. [1] Ulrik Brandes, Thomas Erlebach (eds.). *Network Analysis: Methodological Foundations*. Springer, 2005. <http://books.google.com/books?id=TTNhSm7HYrIC> """ if wiener_index is None: wiener_index = nx.wiener_index(G, weight=weight) if node is not None: after = nx.wiener_index(G.subgraph(set(G) - {node}), weight=weight) return wiener_index - after vitality = partial(closeness_vitality, G, weight=weight, wiener_index=wiener_index) # TODO This can be trivially parallelized. return {v: vitality(node=v) for v in G}