def test_update_fundamental_matrix():
prng = RandomState(20150101)
P = compute_transition_matrix(karate_club_graph())
n = P.shape[0]
order = arange(P.shape[0])
previous_index = prng.choice(order, 1)
previous_node = order[previous_index]
non_absorbing_nodes = chain(range(previous_index),
range(previous_index + 1, n))
non_absorbing_nodes = list(non_absorbing_nodes)
order = order[non_absorbing_nodes]
F = compute_fundamental_matrix(
P[non_absorbing_nodes, :][:, non_absorbing_nodes])
absorbing_nodes = [previous_node]
P_updated = P.copy()
F_updated = F
while P_updated.shape[0] >= 3:
next_node = order[prng.choice(len(order), 1)]
(P_updated, F_updated, order, previous_index) = \
update_fundamental_matrix(P_updated, F_updated, next=next_node,
previous=previous_node,
previous_index=previous_index,
node_order=order)
previous_node = next_node
absorbing_nodes.append(next_node)
non_absorbing_nodes = [x for x in range(n) if x not in absorbing_nodes]
F_slow = compute_fundamental_matrix(
P[non_absorbing_nodes, :][:, non_absorbing_nodes])
error_at_step = sum(sum(F_updated - F_slow).T)[0, 0]
assert abs(error_at_step) < 1e-8, "Error is more than 1e-8."
def test_update_fundamental_matrix():
prng = RandomState(20150101)
P = compute_transition_matrix(karate_club_graph())
n = P.shape[0]
order = arange(P.shape[0])
previous_index = prng.choice(order, 1)
previous_node = order[previous_index]
non_absorbing_nodes = chain(range(previous_index),
range(previous_index + 1, n))
non_absorbing_nodes = list(non_absorbing_nodes)
order = order[non_absorbing_nodes]
F = compute_fundamental_matrix(P[non_absorbing_nodes, :]
[:, non_absorbing_nodes])
absorbing_nodes = [previous_node]
P_updated = P.copy()
F_updated = F
while P_updated.shape[0] >= 3:
next_node = order[prng.choice(len(order), 1)]
(P_updated, F_updated, order, previous_index) = \
update_fundamental_matrix(P_updated, F_updated, next=next_node,
previous=previous_node,
previous_index=previous_index,
node_order=order)
previous_node = next_node
absorbing_nodes.append(next_node)
non_absorbing_nodes = [x for x in range(n) if x not in absorbing_nodes]
F_slow = compute_fundamental_matrix(P[non_absorbing_nodes, :]
[:, non_absorbing_nodes])
error_at_step = sum(sum(F_updated - F_slow).T)[0, 0]
assert abs(error_at_step) < 1e-8, "Error is more than 1e-8."
def test_transition_matrix_with_supernode():
karate_club = karate_club_graph()
karate_club = canonical_relabel_nodes(keep_largest_component(karate_club))
karate_club_super = add_supernode(karate_club, query=[10, 20, 30])
P = compute_transition_matrix(karate_club_super)
for v in [10, 20, 30]:
assert P[-1, v - 1] == 1 / 3
def test_transition_matrix_with_supernode():
karate_club = karate_club_graph()
karate_club = canonical_relabel_nodes(keep_largest_component(karate_club))
karate_club_super = add_supernode(karate_club, query=[10, 20, 30])
P = compute_transition_matrix(karate_club_super)
for v in [10, 20, 30]:
assert P[-1, v - 1] == 1 / 3