U 9v f@s,dZddlmZddlZdgZdddZdS)z Vitality measures. )partialNcloseness_vitalitycsf|dkrtj||d}|dk rDtj|t||h|d}||Stt|||dfdd|DS)aReturns 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. N)weight)r wiener_indexcsi|]}||dqS))node).0vZvitalityr@/tmp/pip-unpacked-wheel-_lngutwb/networkx/algorithms/vitality.py Ksz&closeness_vitality..)nxrZsubgraphsetrr)Grrrafterrr r r s9)NNN)__doc__ functoolsrZnetworkxr __all__rrrrr s