# Copyright (C) 2004-2018 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
#
# Authors: Aric Hagberg (hagberg@lanl.gov)
# Pieter Swart (swart@lanl.gov)
# Sasha Gutfraind (ag362@cornell.edu)
"""Degree centrality measures."""
import networkx as nx
from networkx.utils.decorators import not_implemented_for
__all__ = ['degree_centrality',
'in_degree_centrality',
'out_degree_centrality']
[docs]def degree_centrality(G):
"""Compute the degree centrality for nodes.
The degree centrality for a node v is the fraction of nodes it
is connected to.
Parameters
----------
G : graph
A networkx graph
Returns
-------
nodes : dictionary
Dictionary of nodes with degree centrality as the value.
See Also
--------
betweenness_centrality, load_centrality, eigenvector_centrality
Notes
-----
The degree centrality values are normalized by dividing by the maximum
possible degree in a simple graph n-1 where n is the number of nodes in G.
For multigraphs or graphs with self loops the maximum degree might
be higher than n-1 and values of degree centrality greater than 1
are possible.
"""
if len(G) <= 1:
return {n: 1 for n in G}
s = 1.0 / (len(G) - 1.0)
centrality = {n: d * s for n, d in G.degree()}
return centrality
[docs]@not_implemented_for('undirected')
def in_degree_centrality(G):
"""Compute the in-degree centrality for nodes.
The in-degree centrality for a node v is the fraction of nodes its
incoming edges are connected to.
Parameters
----------
G : graph
A NetworkX graph
Returns
-------
nodes : dictionary
Dictionary of nodes with in-degree centrality as values.
Raises
------
NetworkXNotImplemented:
If G is undirected.
See Also
--------
degree_centrality, out_degree_centrality
Notes
-----
The degree centrality values are normalized by dividing by the maximum
possible degree in a simple graph n-1 where n is the number of nodes in G.
For multigraphs or graphs with self loops the maximum degree might
be higher than n-1 and values of degree centrality greater than 1
are possible.
"""
if len(G) <= 1:
return {n: 1 for n in G}
s = 1.0 / (len(G) - 1.0)
centrality = {n: d * s for n, d in G.in_degree()}
return centrality
[docs]@not_implemented_for('undirected')
def out_degree_centrality(G):
"""Compute the out-degree centrality for nodes.
The out-degree centrality for a node v is the fraction of nodes its
outgoing edges are connected to.
Parameters
----------
G : graph
A NetworkX graph
Returns
-------
nodes : dictionary
Dictionary of nodes with out-degree centrality as values.
Raises
------
NetworkXNotImplemented:
If G is undirected.
See Also
--------
degree_centrality, in_degree_centrality
Notes
-----
The degree centrality values are normalized by dividing by the maximum
possible degree in a simple graph n-1 where n is the number of nodes in G.
For multigraphs or graphs with self loops the maximum degree might
be higher than n-1 and values of degree centrality greater than 1
are possible.
"""
if len(G) <= 1:
return {n: 1 for n in G}
s = 1.0 / (len(G) - 1.0)
centrality = {n: d * s for n, d in G.out_degree()}
return centrality