networkx.algorithms.centrality.harmonic_centrality¶
-
harmonic_centrality
(G, nbunch=None, distance=None)[source]¶ 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 tou
\[C(u) = \sum_{v \neq u} \frac{1}{d(v, u)}\]where
d(v, u)
is the shortest-path distance betweenv
andu
.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 of nodes with harmonic centrality as the value.
- Return type
dictionary
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.