networkx.algorithms.centrality.harmonic_centrality¶
- harmonic_centrality(G, nbunch=None, distance=None, sources=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
.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 insources
tou
instead of from all nodes tou
.Notice that higher values indicate higher centrality.
- Parameters
- Ggraph
A NetworkX graph
- nbunchcontainer (default: all nodes in G)
Container of nodes for which harmonic centrality values are calculated.
- sourcescontainer (default: all nodes in G)
Container of nodes
v
over which reciprocal distances are computed. Nodes not inG
are silently ignored.- distanceedge 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
- nodesdictionary
Dictionary of nodes with harmonic centrality as the value.
See also
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.