ó ,µ[c@ sNdZddlmZddlmZddlZdgZddd„Z dS(s;Functions for computing the harmonic centrality of a graph.iÿÿÿÿ(tdivision(tpartialNtharmonic_centralityc sP|jƒr|jƒ}nttj|d|ƒ‰‡fd†|j|ƒDƒS(sˆCompute harmonic centrality for nodes. Harmonic centrality [1]_ of a node `u` is the sum of the reciprocal of the shortest path distances from all other nodes to `u` .. math:: C(u) = \sum_{v \neq u} \frac{1}{d(v, u)} where `d(v, u)` is the shortest-path distance between `v` and `u`. Notice that higher values indicate higher centrality. Parameters ---------- G : graph A NetworkX graph nbunch : container Container of nodes. If provided harmonic centrality will be computed only over the nodes in nbunch. distance : edge attribute key, optional (default=None) Use the specified edge attribute as the edge distance in shortest path calculations. If `None`, then each edge will have distance equal to 1. Returns ------- nodes : dictionary Dictionary of nodes with harmonic centrality as the value. See Also -------- betweenness_centrality, load_centrality, eigenvector_centrality, degree_centrality, closeness_centrality Notes ----- If the 'distance' keyword is set to an edge attribute key then the shortest-path length will be computed using Dijkstra's algorithm with that edge attribute as the edge weight. References ---------- .. [1] Boldi, Paolo, and Sebastiano Vigna. "Axioms for centrality." Internet Mathematics 10.3-4 (2014): 222-262. tweightc s8i|].}td„ˆd|ƒjƒDƒƒ|“qS(cs s1|]'\}}|dkr%d|ndVqdS(iiN((t.0tvtd((sFlib/python2.7/site-packages/networkx/algorithms/centrality/harmonic.pys Dstsource(tsumtitems(Rtu(tspl(sFlib/python2.7/site-packages/networkx/algorithms/centrality/harmonic.pys Ds (t is_directedtreverseRtnxtshortest_path_lengtht nbunch_iter(tGtnbunchtdistance((R sFlib/python2.7/site-packages/networkx/algorithms/centrality/harmonic.pyRs 0  ( t__doc__t __future__Rt functoolsRtnetworkxRt__all__tNoneR(((sFlib/python2.7/site-packages/networkx/algorithms/centrality/harmonic.pyts