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Version:
3.2.1 ▾
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import pytest
import networkx as nx
from networkx import convert_node_labels_to_integers as cnlti
class TestCliques:
def setup_method(self):
z = [3, 4, 3, 4, 2, 4, 2, 1, 1, 1, 1]
self.G = cnlti(nx.generators.havel_hakimi_graph(z), first_label=1)
self.cl = list(nx.find_cliques(self.G))
H = nx.complete_graph(6)
H = nx.relabel_nodes(H, {i: i + 1 for i in range(6)})
H.remove_edges_from([(2, 6), (2, 5), (2, 4), (1, 3), (5, 3)])
self.H = H
def test_find_cliques1(self):
cl = list(nx.find_cliques(self.G))
rcl = nx.find_cliques_recursive(self.G)
expected = [[2, 6, 1, 3], [2, 6, 4], [5, 4, 7], [8, 9], [10, 11]]
assert sorted(map(sorted, cl)) == sorted(map(sorted, rcl))
assert sorted(map(sorted, cl)) == sorted(map(sorted, expected))
def test_selfloops(self):
self.G.add_edge(1, 1)
cl = list(nx.find_cliques(self.G))
rcl = list(nx.find_cliques_recursive(self.G))
assert set(map(frozenset, cl)) == set(map(frozenset, rcl))
answer = [{2, 6, 1, 3}, {2, 6, 4}, {5, 4, 7}, {8, 9}, {10, 11}]
assert len(answer) == len(cl)
assert all(set(c) in answer for c in cl)
def test_find_cliques2(self):
hcl = list(nx.find_cliques(self.H))
assert sorted(map(sorted, hcl)) == [[1, 2], [1, 4, 5, 6], [2, 3], [3, 4, 6]]
def test_find_cliques3(self):
# all cliques are [[2, 6, 1, 3], [2, 6, 4], [5, 4, 7], [8, 9], [10, 11]]
cl = list(nx.find_cliques(self.G, [2]))
rcl = nx.find_cliques_recursive(self.G, [2])
expected = [[2, 6, 1, 3], [2, 6, 4]]
assert sorted(map(sorted, rcl)) == sorted(map(sorted, expected))
assert sorted(map(sorted, cl)) == sorted(map(sorted, expected))
cl = list(nx.find_cliques(self.G, [2, 3]))
rcl = nx.find_cliques_recursive(self.G, [2, 3])
expected = [[2, 6, 1, 3]]
assert sorted(map(sorted, rcl)) == sorted(map(sorted, expected))
assert sorted(map(sorted, cl)) == sorted(map(sorted, expected))
cl = list(nx.find_cliques(self.G, [2, 6, 4]))
rcl = nx.find_cliques_recursive(self.G, [2, 6, 4])
expected = [[2, 6, 4]]
assert sorted(map(sorted, rcl)) == sorted(map(sorted, expected))
assert sorted(map(sorted, cl)) == sorted(map(sorted, expected))
cl = list(nx.find_cliques(self.G, [2, 6, 4]))
rcl = nx.find_cliques_recursive(self.G, [2, 6, 4])
expected = [[2, 6, 4]]
assert sorted(map(sorted, rcl)) == sorted(map(sorted, expected))
assert sorted(map(sorted, cl)) == sorted(map(sorted, expected))
with pytest.raises(ValueError):
list(nx.find_cliques(self.G, [2, 6, 4, 1]))
with pytest.raises(ValueError):
list(nx.find_cliques_recursive(self.G, [2, 6, 4, 1]))
def test_number_of_cliques(self):
G = self.G
assert nx.number_of_cliques(G, 1) == 1
assert list(nx.number_of_cliques(G, [1]).values()) == [1]
assert list(nx.number_of_cliques(G, [1, 2]).values()) == [1, 2]
assert nx.number_of_cliques(G, [1, 2]) == {1: 1, 2: 2}
assert nx.number_of_cliques(G, 2) == 2
assert nx.number_of_cliques(G) == {
1: 1,
2: 2,
3: 1,
4: 2,
5: 1,
6: 2,
7: 1,
8: 1,
9: 1,
10: 1,
11: 1,
}
assert nx.number_of_cliques(G, nodes=list(G)) == {
1: 1,
2: 2,
3: 1,
4: 2,
5: 1,
6: 2,
7: 1,
8: 1,
9: 1,
10: 1,
11: 1,
}
assert nx.number_of_cliques(G, nodes=[2, 3, 4]) == {2: 2, 3: 1, 4: 2}
assert nx.number_of_cliques(G, cliques=self.cl) == {
1: 1,
2: 2,
3: 1,
4: 2,
5: 1,
6: 2,
7: 1,
8: 1,
9: 1,
10: 1,
11: 1,
}
assert nx.number_of_cliques(G, list(G), cliques=self.cl) == {
1: 1,
2: 2,
3: 1,
4: 2,
5: 1,
6: 2,
7: 1,
8: 1,
9: 1,
10: 1,
11: 1,
}
def test_node_clique_number(self):
G = self.G
assert nx.node_clique_number(G, 1) == 4
assert list(nx.node_clique_number(G, [1]).values()) == [4]
assert list(nx.node_clique_number(G, [1, 2]).values()) == [4, 4]
assert nx.node_clique_number(G, [1, 2]) == {1: 4, 2: 4}
assert nx.node_clique_number(G, 1) == 4
assert nx.node_clique_number(G) == {
1: 4,
2: 4,
3: 4,
4: 3,
5: 3,
6: 4,
7: 3,
8: 2,
9: 2,
10: 2,
11: 2,
}
assert nx.node_clique_number(G, cliques=self.cl) == {
1: 4,
2: 4,
3: 4,
4: 3,
5: 3,
6: 4,
7: 3,
8: 2,
9: 2,
10: 2,
11: 2,
}
assert nx.node_clique_number(G, [1, 2], cliques=self.cl) == {1: 4, 2: 4}
assert nx.node_clique_number(G, 1, cliques=self.cl) == 4
def test_make_clique_bipartite(self):
G = self.G
B = nx.make_clique_bipartite(G)
assert sorted(B) == [-5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
# Project onto the nodes of the original graph.
H = nx.projected_graph(B, range(1, 12))
assert H.adj == G.adj
# Project onto the nodes representing the cliques.
H1 = nx.projected_graph(B, range(-5, 0))
# Relabel the negative numbers as positive ones.
H1 = nx.relabel_nodes(H1, {-v: v for v in range(1, 6)})
assert sorted(H1) == [1, 2, 3, 4, 5]
def test_make_max_clique_graph(self):
"""Tests that the maximal clique graph is the same as the bipartite
clique graph after being projected onto the nodes representing the
cliques.
"""
G = self.G
B = nx.make_clique_bipartite(G)
# Project onto the nodes representing the cliques.
H1 = nx.projected_graph(B, range(-5, 0))
# Relabel the negative numbers as nonnegative ones, starting at
# 0.
H1 = nx.relabel_nodes(H1, {-v: v - 1 for v in range(1, 6)})
H2 = nx.make_max_clique_graph(G)
assert H1.adj == H2.adj
def test_directed(self):
with pytest.raises(nx.NetworkXNotImplemented):
next(nx.find_cliques(nx.DiGraph()))
def test_find_cliques_trivial(self):
G = nx.Graph()
assert sorted(nx.find_cliques(G)) == []
assert sorted(nx.find_cliques_recursive(G)) == []
def test_make_max_clique_graph_create_using(self):
G = nx.Graph([(1, 2), (3, 1), (4, 1), (5, 6)])
E = nx.Graph([(0, 1), (0, 2), (1, 2)])
E.add_node(3)
assert nx.is_isomorphic(nx.make_max_clique_graph(G, create_using=nx.Graph), E)
class TestEnumerateAllCliques:
def test_paper_figure_4(self):
# Same graph as given in Fig. 4 of paper enumerate_all_cliques is
# based on.
# http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1559964&isnumber=33129
G = nx.Graph()
edges_fig_4 = [
("a", "b"),
("a", "c"),
("a", "d"),
("a", "e"),
("b", "c"),
("b", "d"),
("b", "e"),
("c", "d"),
("c", "e"),
("d", "e"),
("f", "b"),
("f", "c"),
("f", "g"),
("g", "f"),
("g", "c"),
("g", "d"),
("g", "e"),
]
G.add_edges_from(edges_fig_4)
cliques = list(nx.enumerate_all_cliques(G))
clique_sizes = list(map(len, cliques))
assert sorted(clique_sizes) == clique_sizes
expected_cliques = [
["a"],
["b"],
["c"],
["d"],
["e"],
["f"],
["g"],
["a", "b"],
["a", "b", "d"],
["a", "b", "d", "e"],
["a", "b", "e"],
["a", "c"],
["a", "c", "d"],
["a", "c", "d", "e"],
["a", "c", "e"],
["a", "d"],
["a", "d", "e"],
["a", "e"],
["b", "c"],
["b", "c", "d"],
["b", "c", "d", "e"],
["b", "c", "e"],
["b", "c", "f"],
["b", "d"],
["b", "d", "e"],
["b", "e"],
["b", "f"],
["c", "d"],
["c", "d", "e"],
["c", "d", "e", "g"],
["c", "d", "g"],
["c", "e"],
["c", "e", "g"],
["c", "f"],
["c", "f", "g"],
["c", "g"],
["d", "e"],
["d", "e", "g"],
["d", "g"],
["e", "g"],
["f", "g"],
["a", "b", "c"],
["a", "b", "c", "d"],
["a", "b", "c", "d", "e"],
["a", "b", "c", "e"],
]
assert sorted(map(sorted, cliques)) == sorted(map(sorted, expected_cliques))