btj ZdZddlmZddlZdgZejdddZdS) z;Functions for computing the harmonic centrality of a graph.)partialNharmonic_centralitydistance) edge_attrsc<t|||n|j}t|||n|j}d|D}d}t|t|kr0d}||}}t j|rt j|d}ttj||}|D]H}||}| D]&\} } | dkr| |vr||r|n| xxd| z z cc<'I|S) a%Compute 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`. If `sources` is given as an argument, the returned harmonic centrality values are calculated as the sum of the reciprocals of the shortest path distances from the nodes specified in `sources` to `u` instead of from all nodes to `u`. Notice that higher values indicate higher centrality. Parameters ---------- G : graph A NetworkX graph nbunch : container (default: all nodes in G) Container of nodes for which harmonic centrality values are calculated. sources : container (default: all nodes in G) Container of nodes `v` over which reciprocal distances are computed. Nodes not in `G` are silently ignored. 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. Nci|]}|dS)r).0us e/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/networkx/algorithms/centrality/harmonic.py z'harmonic_centrality..Gs'''1!Q'''FT)copy)weightr) set nbunch_iternodeslennx is_directedreversershortest_path_lengthitems) Gnbunchrsources centrality transposedsplvdistr d_uvs r rr sHt&*<v&&&!' J JFG,?!--(((QWMMG'''''JJ 6{{S\\!! !6 >!   * 15)))A ")1X > > >C ??s1vvzz|| ? ?GAtqyyQ&[[ 111222a$h>222 ? r)NNN)__doc__ functoolsrnetworkxr__all__ _dispatchablerr rr r)srAA !Z(((MMM)(MMMr