def METHOD_NAME(length, loops=True, directed=False):
    """Creates two complete undirected graphs of size `length`
    attached by a single edge."""
    edges = []
    # Two complete graphs
    for cluster in range(2):
        for i in range(length):
            for j in range(i + 1, length):
                edges.append(
                    ("{}:{}".format(cluster, i), "{}:{}".format(cluster, j))
                )
    # Attach at one node
    edges.append(("0:0", "1:0"))
    graph = Graph(directed=directed, edges=edges)
    if loops:
        graph.add_loops()
    return graph