U md @s,dZddlmZddlZdgZdddZdS)z;Functions for computing the harmonic centrality of a graph.)partialNharmonic_centralityc Cs|dk rt||nt|j}|dk r6t||n|j}ttj||d}dd|D}|D]B}||}||D]*}||} | dkrqt||d| 7<qtq^|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. N)weightcSsi|] }|dqS)r).0urr`/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/networkx/algorithms/centrality/harmonic.py Fsz'harmonic_centrality..r)setZ nbunch_iterZnodesrnxZshortest_path_length intersection) GZnbunchZdistancesourcesZsplZ centralityvdistrdrrrr s9 )NNN)__doc__ functoolsrZnetworkxr __all__rrrrrs