def statistic(G):
    parameter = lambda G: G.clique_number()
    return statistic_parameter(G, parameter)

@cached_function
def statistic_parameter(G, parameter):
    """
    The number of edges that can be added without modifying the value
    of `parameter`.

    We assume that the value of `parameter` does not decrease when
    adding edges.
    """
    D = parameter(G)
    E = [(u, v) for u, v in Subsets(G.vertices(), 2) if not G.has_edge(u, v)]
    l = [0]
    for u, v in E:
        H = G.copy(immutable=False)
        H.add_edge(u, v)
        H = H.canonical_label().copy(immutable=True)
        if parameter(H) <= D:
            l.append(statistic_parameter(H, parameter)+1)
    return max(l)