def modularity(adjacency,communities):
    a=np.asarray(adjacency);degrees=a.sum(axis=1);twom=degrees.sum()
    if twom==0:raise ValueError('positive edge count required')
    B=a-np.outer(degrees,degrees)/twom
    return sum(B[np.ix_(group,group)].sum() for group in communities)/twom

best_score = -np.inf
best_partition = None
for candidate in community_partitions:
    value = modularity(adjacency_matrix, candidate)
    if value > best_score:
        best_score, best_partition = value, candidate
print(best_partition, best_score)

def partitions(items):
    if not items:
        yield [];return
    first,*rest=items
    for part in partitions(rest):
        yield [[first]]+[g.copy() for g in part]
        for j in range(len(part)):
            new=[g.copy() for g in part];new[j]=[first]+new[j];yield new

candidates = list(partitions(list(range(len(adjacency_matrix)))))
best_partition = max(candidates, key=lambda p: modularity(adjacency_matrix, p))
print(len(candidates), best_partition, modularity(adjacency_matrix, best_partition))