def directed_graph_has_odd_automorphism(g):
n = len(g)
edges = g.edges()
G = DiGraph([list(range(n)), edges])
for sigma in G.automorphism_group().gens(
): # NOTE: it suffices to check generators
edge_permutation = [
tuple([sigma(edge[0]), sigma(edge[1])]) for edge in edges
]
index_permutation = [edges.index(e) for e in edge_permutation]
if selection_sort(index_permutation) == -1:
return True
return False
def formality_graph_has_odd_automorphism(g):
n = len(g)
edges = g.edges()
partition = [[v] for v in range(g.num_ground_vertices())] + [
list(
range(g.num_ground_vertices(),
g.num_ground_vertices() + g.num_aerial_vertices()))
]
G = DiGraph([list(range(n)), edges])
for sigma in G.automorphism_group(partition=partition).gens(
): # NOTE: it suffices to check generators
edge_permutation = [
tuple([sigma(edge[0]), sigma(edge[1])]) for edge in edges
]
index_permutation = [edges.index(e) for e in edge_permutation]
if selection_sort(index_permutation) == -1:
return True
return False
