def is_total_order(graph: DiGraph) -> bool:
reflexive = is_reflexive(graph)
anti_symmetric = is_anti_symmetric(graph)
transitive = is_transitive(graph)
all_relatione = all(
graph.has_edge(x, y) and graph.has_edge(y, x)
for x, y in get_set_combination(graph.nodes))
return reflexive and anti_symmetric and transitive and all_relatione
def generate_relations(
nodes: Set[int],
condition: Callable[[int, int], bool],
inverse: bool = False,
) -> Iterator[Tuple[int, int]]:
for node_x, node_y in get_set_combination(nodes):
if condition(node_x, node_y):
if inverse:
yield (node_y, node_x)
continue
yield (node_x, node_y)
def get_all_mcs(graph: DiGraph) -> Iterator[Tuple[Set[Any], Any]]:
for node_x, node_y in get_set_combination(graph.nodes):
yield ({node_x, node_y}, _get_mcs(graph, node_x, node_y))
def is_not_transitive(graph: DiGraph) -> bool:
return any(not graph.has_edge(x, z)
for x, y in get_set_combination(graph.nodes)
if x != y and graph.has_edge(x, y) for z in graph.adj[y]
if y != z)
def is_lattice(graph: DiGraph) -> bool:
nodes = graph.nodes
return all(
get_mcs(graph, x, y) and get_mci(graph, x, y)
for x, y in get_set_combination(nodes) if x != y)