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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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@nx._dispatchable(edge_attrs="weight") |
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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, wiener_index=wiener_index) |
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return {v: vitality(node=v) for v in G} |
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