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1"""
2Vitality measures.
3"""
5from functools import partial
7import networkx as nx
9__all__ = ["closeness_vitality"]
12@nx._dispatchable(edge_attrs="weight")
13def closeness_vitality(G, node=None, weight=None, wiener_index=None):
14 """Returns the closeness vitality for nodes in the graph.
16 The *closeness vitality* of a node, defined in Section 3.6.2 of [1],
17 is the change in the sum of distances between all node pairs when
18 excluding that node.
20 Parameters
21 ----------
22 G : NetworkX graph
23 A strongly-connected graph.
25 weight : string
26 The name of the edge attribute used as weight. This is passed
27 directly to the :func:`~networkx.wiener_index` function.
29 node : object
30 If specified, only the closeness vitality for this node will be
31 returned. Otherwise, a dictionary mapping each node to its
32 closeness vitality will be returned.
34 Other parameters
35 ----------------
36 wiener_index : number
37 If you have already computed the Wiener index of the graph
38 `G`, you can provide that value here. Otherwise, it will be
39 computed for you.
41 Returns
42 -------
43 dictionary or float
44 If `node` is None, this function returns a dictionary
45 with nodes as keys and closeness vitality as the
46 value. Otherwise, it returns only the closeness vitality for the
47 specified `node`.
49 The closeness vitality of a node may be negative infinity if
50 removing that node would disconnect the graph.
52 Examples
53 --------
54 >>> G = nx.cycle_graph(3)
55 >>> nx.closeness_vitality(G)
56 {0: 2.0, 1: 2.0, 2: 2.0}
58 See Also
59 --------
60 closeness_centrality
62 References
63 ----------
64 .. [1] Ulrik Brandes, Thomas Erlebach (eds.).
65 *Network Analysis: Methodological Foundations*.
66 Springer, 2005.
67 <http://books.google.com/books?id=TTNhSm7HYrIC>
69 """
70 if wiener_index is None:
71 wiener_index = nx.wiener_index(G, weight=weight)
72 if node is not None:
73 after = nx.wiener_index(G.subgraph(set(G) - {node}), weight=weight)
74 return wiener_index - after
75 vitality = partial(closeness_vitality, G, weight=weight, wiener_index=wiener_index)
76 return {v: vitality(node=v) for v in G}