Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Source code for networkx.algorithms.centrality.degree_alg

"""
Degree centrality measures.

"""
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
__author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
'Pieter Swart (swart@lanl.gov)',
'Sasha Gutfraind (ag362@cornell.edu)'])

__all__ = ['degree_centrality',
'in_degree_centrality',
'out_degree_centrality']

import networkx as nx

[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.

--------

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.
"""
centrality={}
s=1.0/(len(G)-1.0)
centrality=dict((n,d*s) for n,d in G.degree_iter())
return centrality

[docs]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.

--------
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 not G.is_directed():
raise nx.NetworkXError(\
"in_degree_centrality() not defined for undirected graphs.")
centrality={}
s=1.0/(len(G)-1.0)
centrality=dict((n,d*s) for n,d in G.in_degree_iter())
return centrality

[docs]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.

--------
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 not G.is_directed():
raise nx.NetworkXError(\
"out_degree_centrality() not defined for undirected graphs.")
centrality={}
s=1.0/(len(G)-1.0)
centrality=dict((n,d*s) for n,d in G.out_degree_iter())
return centrality