@cached_function
def partition(n):
    """
    Return the set partition of biconnected graphs having the same SEPs.
    """
    p = {}
    g = {}
    lG = [G.canonical_label().copy(immutable=True) for G in graphs(n)]
    for G in lG:
        Q = G.symmetric_edge_polytope()
        for P in p.keys():
            if P.is_combinatorially_isomorphic(Q):
                p[P].append(G)
                g[G] = P
                break
        else:
            p[Q] = [G]
            g[G] = Q
    
    return {G: len(p[g[G]]) for G in lG}

def statistic(G):
    G = G.canonical_label().copy(immutable=True)
    return partition(G.num_verts())[G]