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# Source code for networkx.algorithms.centrality.degree_alg

#    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. 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