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Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

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Source code for networkx.algorithms.centrality.degree_alg

"""Degree centrality measures."""
from networkx.utils.decorators import not_implemented_for

__all__ = ["degree_centrality", "in_degree_centrality", "out_degree_centrality"]


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


@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


@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