| | """Functions for computing the harmonic centrality of a graph.""" |
| | from functools import partial |
| |
|
| | import networkx as nx |
| |
|
| | __all__ = ["harmonic_centrality"] |
| |
|
| |
|
| | @nx._dispatchable(edge_attrs="distance") |
| | 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: |
| | continue |
| | centrality[u] += 1 / d |
| |
|
| | return centrality |
| |
|
