Source code for networkx.algorithms.approximation.clustering_coefficient

from networkx.utils import not_implemented_for, py_random_state

__all__ = ["average_clustering"]


@py_random_state(2)
@not_implemented_for("directed")
def average_clustering(G, trials=1000, seed=None):
    r"""Estimates the average clustering coefficient of G.

    The local clustering of each node in `G` is the fraction of triangles
    that actually exist over all possible triangles in its neighborhood.
    The average clustering coefficient of a graph `G` is the mean of
    local clusterings.

    This function finds an approximate average clustering coefficient
    for G by repeating `n` times (defined in `trials`) the following
    experiment: choose a node at random, choose two of its neighbors
    at random, and check if they are connected. The approximate
    coefficient is the fraction of triangles found over the number
    of trials [1]_.

    Parameters
    ----------
    G : NetworkX graph

    trials : integer
        Number of trials to perform (default 1000).

    seed : integer, random_state, or None (default)
        Indicator of random number generation state.
        See :ref:`Randomness<randomness>`.

    Returns
    -------
    c : float
        Approximated average clustering coefficient.

    Examples
    --------
    >>> from networkx.algorithms import approximation
    >>> G = nx.erdos_renyi_graph(10, 0.2, seed=10)
    >>> approximation.average_clustering(G, trials=1000, seed=10)
    0.214

    References
    ----------
    .. [1] Schank, Thomas, and Dorothea Wagner. Approximating clustering
       coefficient and transitivity. Universität Karlsruhe, Fakultät für
       Informatik, 2004.
       https://doi.org/10.5445/IR/1000001239

    """
    n = len(G)
    triangles = 0
    nodes = list(G)
    for i in [int(seed.random() * n) for i in range(trials)]:
        nbrs = list(G[nodes[i]])
        if len(nbrs) < 2:
            continue
        u, v = seed.sample(nbrs, 2)
        if u in G[v]:
            triangles += 1
    return triangles / trials