def closed_neighbourhood(G, v):
    return G[v] + [v]

def closed_neighbourhood_set(G, lv):
    return set([u for v in lv for u in G[v]]).union(lv)
    
def private_neighbourhood(G, v, S):
    return set(closed_neighbourhood(G, v)) - closed_neighbourhood_set(G, set(S) - set([v]))

def is_irredundant(G, S):
    return all(private_neighbourhood(G, v, S) for v in S)

def maximal_irredundant_sets(G):
    V = set(G.vertices())
    def children(S):
        for v in V - S:
            S1 = S.union([v])
            if is_irredundant(G, S1):
                yield S1
    R = RecursivelyEnumeratedSet([frozenset()], children)
    return Poset(R.to_digraph()).maximal_elements()

def statistic(G):
    return min(len(S) for S in maximal_irredundant_sets(G))