def test_is_output_clique(self, dim):
"""Test that the output subgraph is a valid clique, in this case the maximum clique
in a lollipop graph"""
graph = nx.lollipop_graph(dim, dim)
subgraph = list(range(2 * dim)) # subgraph is the entire graph
resized = clique.shrink(subgraph, graph)
assert clique.is_clique(graph.subgraph(resized))
assert resized == list(range(dim))
def test_c_1_swap_to_clique(self, dim):
"""Tests that :math:`c_1` set gives a valid clique after swapping """
A = nx.complete_graph(dim)
A.remove_edge(0, 1)
S = list(range(1, dim))
c1 = clique.c_1(S, A)
swap_nodes = c1[0]
S.remove(swap_nodes[0])
S.append(swap_nodes[1])
assert clique.is_clique(A.subgraph(S))
for s in samples:
uniform = list(np.random.choice(24, 8,
replace=False)) # generates uniform sample
GBS_dens.append(nx.density(TA_graph.subgraph(s)))
u_dens.append(nx.density(TA_graph.subgraph(uniform)))
print("GBS mean density = {:.4f}".format(np.mean(GBS_dens)))
print("Uniform mean density = {:.4f}".format(np.mean(u_dens)))
##############################################################################
# Those look like great GBS samples 💪! To obtain cliques, we shrink the samples by greedily
# removing nodes with low degree until a clique is found.
shrunk = [clique.shrink(s, TA_graph) for s in samples]
print(clique.is_clique(TA_graph.subgraph(shrunk[0])))
##############################################################################
# Let's take a look at some of these cliques. What are the clique sizes in the first ten samples?
# What is the average clique size? How about the largest and smallest clique size?
clique_sizes = [len(s) for s in shrunk]
print("First ten clique sizes = ", clique_sizes[:10])
print("Average clique size = {:.3f}".format(np.mean(clique_sizes)))
print("Maximum clique size = ", np.max(clique_sizes))
print("Minimum clique size = ", np.min(clique_sizes))
##############################################################################
# Even in the first few samples, we've already identified larger cliques than the 4-node clique
# we studied before. Awesome! Indeed, this simple shrinking strategy gives cliques with average
# size of roughly five. We can enlarge these cliques by searching for larger cliques in their
def test_no_false_positives(self, dim):
"""Tests that non-cliques are labelled as such"""
g = nx.empty_graph(dim)
assert not clique.is_clique(g)
def test_no_false_negatives(self, dim):
"""Tests that cliques are labelled as such"""
g = nx.complete_graph(dim)
assert clique.is_clique(g)