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1"""Degree centrality measures."""
3import networkx as nx
4from networkx.utils.decorators import not_implemented_for
6__all__ = ["degree_centrality", "in_degree_centrality", "out_degree_centrality"]
9@nx._dispatchable
10def degree_centrality(G):
11 """Compute the degree centrality for nodes.
13 The degree centrality for a node v is the fraction of nodes it
14 is connected to.
16 Parameters
17 ----------
18 G : graph
19 A networkx graph
21 Returns
22 -------
23 nodes : dictionary
24 Dictionary of nodes with degree centrality as the value.
26 Examples
27 --------
28 >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
29 >>> nx.degree_centrality(G)
30 {0: 1.0, 1: 1.0, 2: 0.6666666666666666, 3: 0.6666666666666666}
32 See Also
33 --------
34 betweenness_centrality, load_centrality, eigenvector_centrality
36 Notes
37 -----
38 The degree centrality values are normalized by dividing by the maximum
39 possible degree in a simple graph n-1 where n is the number of nodes in G.
41 For multigraphs or graphs with self loops the maximum degree might
42 be higher than n-1 and values of degree centrality greater than 1
43 are possible.
44 """
45 if len(G) <= 1:
46 return {n: 1 for n in G}
48 s = 1.0 / (len(G) - 1.0)
49 centrality = {n: d * s for n, d in G.degree()}
50 return centrality
53@not_implemented_for("undirected")
54@nx._dispatchable
55def in_degree_centrality(G):
56 """Compute the in-degree centrality for nodes.
58 The in-degree centrality for a node v is the fraction of nodes its
59 incoming edges are connected to.
61 Parameters
62 ----------
63 G : graph
64 A NetworkX graph
66 Returns
67 -------
68 nodes : dictionary
69 Dictionary of nodes with in-degree centrality as values.
71 Raises
72 ------
73 NetworkXNotImplemented
74 If G is undirected.
76 Examples
77 --------
78 >>> G = nx.DiGraph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
79 >>> nx.in_degree_centrality(G)
80 {0: 0.0, 1: 0.3333333333333333, 2: 0.6666666666666666, 3: 0.6666666666666666}
82 See Also
83 --------
84 degree_centrality, out_degree_centrality
86 Notes
87 -----
88 The degree centrality values are normalized by dividing by the maximum
89 possible degree in a simple graph n-1 where n is the number of nodes in G.
91 For multigraphs or graphs with self loops the maximum degree might
92 be higher than n-1 and values of degree centrality greater than 1
93 are possible.
94 """
95 if len(G) <= 1:
96 return {n: 1 for n in G}
98 s = 1.0 / (len(G) - 1.0)
99 centrality = {n: d * s for n, d in G.in_degree()}
100 return centrality
103@not_implemented_for("undirected")
104@nx._dispatchable
105def out_degree_centrality(G):
106 """Compute the out-degree centrality for nodes.
108 The out-degree centrality for a node v is the fraction of nodes its
109 outgoing edges are connected to.
111 Parameters
112 ----------
113 G : graph
114 A NetworkX graph
116 Returns
117 -------
118 nodes : dictionary
119 Dictionary of nodes with out-degree centrality as values.
121 Raises
122 ------
123 NetworkXNotImplemented
124 If G is undirected.
126 Examples
127 --------
128 >>> G = nx.DiGraph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
129 >>> nx.out_degree_centrality(G)
130 {0: 1.0, 1: 0.6666666666666666, 2: 0.0, 3: 0.0}
132 See Also
133 --------
134 degree_centrality, in_degree_centrality
136 Notes
137 -----
138 The degree centrality values are normalized by dividing by the maximum
139 possible degree in a simple graph n-1 where n is the number of nodes in G.
141 For multigraphs or graphs with self loops the maximum degree might
142 be higher than n-1 and values of degree centrality greater than 1
143 are possible.
144 """
145 if len(G) <= 1:
146 return {n: 1 for n in G}
148 s = 1.0 / (len(G) - 1.0)
149 centrality = {n: d * s for n, d in G.out_degree()}
150 return centrality