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| """Functions for computing the harmonic centrality of a graph.""" | |
| from functools import partial | |
| import networkx as nx | |
| __all__ = ["harmonic_centrality"] | |
| def harmonic_centrality(G, nbunch=None, distance=None, sources=None): | |
| r"""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. | |
| """ | |
| nbunch = set(G.nbunch_iter(nbunch)) if nbunch is not None else set(G.nodes) | |
| sources = set(G.nbunch_iter(sources)) if sources is not None else G.nodes | |
| spl = partial(nx.shortest_path_length, G, weight=distance) | |
| centrality = {u: 0 for u in nbunch} | |
| for v in sources: | |
| dist = spl(v) | |
| for u in nbunch.intersection(dist): | |
| d = dist[u] | |
| if d == 0: # handle u == v and edges with 0 weight | |
| continue | |
| centrality[u] += 1 / d | |
| return centrality | |