63 lines
1.8 KiB
Python
63 lines
1.8 KiB
Python
"""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):
|
|
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`.
|
|
|
|
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
|
|
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.
|
|
"""
|
|
if G.is_directed():
|
|
G = G.reverse()
|
|
spl = partial(nx.shortest_path_length, G, weight=distance)
|
|
return {
|
|
u: sum(1 / d if d > 0 else 0 for v, d in spl(source=u).items())
|
|
for u in G.nbunch_iter(nbunch)
|
|
}
|