88 lines
2.6 KiB
Python
88 lines
2.6 KiB
Python
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# Copyright (C) 2010 by
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# Aric Hagberg (hagberg@lanl.gov)
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# Renato Fabbri
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# Copyright (C) 2012 by
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# Aric Hagberg <hagberg@lanl.gov>
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# Dan Schult <dschult@colgate.edu>
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# Pieter Swart <swart@lanl.gov>
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# Copyright (C) 2016-2019 by NetworkX developers.
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#
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# All rights reserved.
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# BSD license.
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"""
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Vitality measures.
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"""
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from functools import partial
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import networkx as nx
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__all__ = ['closeness_vitality']
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def closeness_vitality(G, node=None, weight=None, wiener_index=None):
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"""Returns the closeness vitality for nodes in the graph.
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The *closeness vitality* of a node, defined in Section 3.6.2 of [1],
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is the change in the sum of distances between all node pairs when
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excluding that node.
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Parameters
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----------
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G : NetworkX graph
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A strongly-connected graph.
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weight : string
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The name of the edge attribute used as weight. This is passed
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directly to the :func:`~networkx.wiener_index` function.
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node : object
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If specified, only the closeness vitality for this node will be
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returned. Otherwise, a dictionary mapping each node to its
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closeness vitality will be returned.
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Other parameters
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----------------
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wiener_index : number
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If you have already computed the Wiener index of the graph
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`G`, you can provide that value here. Otherwise, it will be
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computed for you.
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Returns
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-------
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dictionary or float
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If `node` is None, this function returns a dictionary
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with nodes as keys and closeness vitality as the
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value. Otherwise, it returns only the closeness vitality for the
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specified `node`.
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The closeness vitality of a node may be negative infinity if
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removing that node would disconnect the graph.
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Examples
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--------
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>>> G = nx.cycle_graph(3)
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>>> nx.closeness_vitality(G)
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{0: 2.0, 1: 2.0, 2: 2.0}
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See Also
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--------
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closeness_centrality
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References
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----------
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.. [1] Ulrik Brandes, Thomas Erlebach (eds.).
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*Network Analysis: Methodological Foundations*.
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Springer, 2005.
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<http://books.google.com/books?id=TTNhSm7HYrIC>
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"""
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if wiener_index is None:
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wiener_index = nx.wiener_index(G, weight=weight)
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if node is not None:
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after = nx.wiener_index(G.subgraph(set(G) - {node}), weight=weight)
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return wiener_index - after
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vitality = partial(closeness_vitality, G, weight=weight,
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wiener_index=wiener_index)
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# TODO This can be trivially parallelized.
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return {v: vitality(node=v) for v in G}
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