# Source code for networkx.algorithms.centrality.degree_alg

```"""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]@nx._dispatch
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}

--------

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]@nx._dispatch
@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.

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}

--------
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]@nx._dispatch
@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.

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}

--------
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
```