Original from https://gist.github.com/tpoisot/8582648. Update the counter to the last version of python available, 3.13. Find it super useful.

network_motif_counter.py

import networkx as nx
import numpy as np
import itertools

# We define each S* motif as a directed graph in networkx
motifs = {
    'S1': nx.DiGraph([(1, 2), (2, 3)]),
    'S2': nx.DiGraph([(1, 2), (1, 3), (2, 3)]),
    'S3': nx.DiGraph([(1, 2), (2, 3), (3, 1)]),
    'S4': nx.DiGraph([(1, 2), (3, 2)]),
    'S5': nx.DiGraph([(1, 2), (1, 3)])
    }


def mcounter(gr, mo):
    """Counts motifs in a directed graph

    :param gr: A ``DiGraph`` object
    :param mo: A ``dict`` of motifs to count
    :returns: A ``dict`` with the number of each motifs, with the same keys as ``mo``

    This function is actually rather simple. It will extract all 3-grams from
    the original graph, and look for isomorphisms in the motifs contained
    in a dictionary. The returned object is a ``dict`` with the number of
    times each motif was found.::

        >>> print mcounter(gr, mo)
        {'S1': 4, 'S3': 0, 'S2': 1, 'S5': 0, 'S4': 3}

    """
    # This function will take each possible subgraphs of gr of size 3, then
    # compare them to the mo dict using .subgraph() and is_isomorphic

    # This line simply creates a dictionary with 0 for all values, and the
    # motif names as keys

    nodes = gr.nodes()

    # We use iterools.product to have all combinations of three nodes in the
    # original graph. Then we filter combinations with non-unique nodes,
    # because the motifs do not account for self-consumption.

    triplets = list(itertools.product(*[nodes, nodes, nodes]))
    triplets = [t for t in triplets if len(set(t)) == 3]
    triplets = map(lambda x: x.tolist(), map(np.sort, triplets))
    u_triplets = []
    [u_triplets.append(trip) for trip in triplets if not u_triplets.count(trip)]

    # The for each each of the triplets, we (i) take its subgraph, and compare
    # it to all fo the possible motifs

    mcount = {k: 0 for k in mo.keys()}
    for trip in u_triplets:
        for k, v in mo.items():
            if nx.is_isomorphic(v, gr.subgraph(trip)):
                mcount[k] += 1

    return mcount