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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

#    Copyright (C) 2004-2019 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#
# 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.

--------

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.

--------
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.

--------
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