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+"""Degree centrality measures."""
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = ["degree_centrality", "in_degree_centrality", "out_degree_centrality"]
+
+
+@nx._dispatchable
+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.
+
+ Examples
+ --------
+ >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+ >>> nx.degree_centrality(G)
+ {0: 1.0, 1: 1.0, 2: 0.6666666666666666, 3: 0.6666666666666666}
+
+ 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
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+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.
+
+ Examples
+ --------
+ >>> G = nx.DiGraph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+ >>> nx.in_degree_centrality(G)
+ {0: 0.0, 1: 0.3333333333333333, 2: 0.6666666666666666, 3: 0.6666666666666666}
+
+ 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
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+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.
+
+ Examples
+ --------
+ >>> G = nx.DiGraph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+ >>> nx.out_degree_centrality(G)
+ {0: 1.0, 1: 0.6666666666666666, 2: 0.0, 3: 0.0}
+
+ 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