#!/usr/bin/env python
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, dict([(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_clique_number(self):
G = self.G
assert nx.graph_clique_number(G) == 4
assert nx.graph_clique_number(G, cliques=self.cl) == 4
def test_clique_number2(self):
G = nx.Graph()
G.add_nodes_from([1, 2, 3])
assert nx.graph_clique_number(G) == 1
def test_clique_number3(self):
G = nx.Graph()
assert nx.graph_clique_number(G) == 0
def test_number_of_cliques(self):
G = self.G
assert nx.graph_number_of_cliques(G) == 5
assert nx.graph_number_of_cliques(G, cliques=self.cl) == 5
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})
def test_cliques_containing_node(self):
G = self.G
assert (nx.cliques_containing_node(G, 1) ==
[[2, 6, 1, 3]])
assert (list(nx.cliques_containing_node(G, [1]).values()) ==
[[[2, 6, 1, 3]]])
assert ([sorted(c) for c in list(nx.cliques_containing_node(G, [1, 2]).values())] ==
[[[2, 6, 1, 3]], [[2, 6, 1, 3], [2, 6, 4]]])
result = nx.cliques_containing_node(G, [1, 2])
for k, v in result.items():
result[k] = sorted(v)
assert (result ==
{1: [[2, 6, 1, 3]], 2: [[2, 6, 1, 3], [2, 6, 4]]})
assert (nx.cliques_containing_node(G, 1) ==
[[2, 6, 1, 3]])
expected = [{2, 6, 1, 3}, {2, 6, 4}]
answer = [set(c) for c in nx.cliques_containing_node(G, 2)]
assert answer in (expected, list(reversed(expected)))
answer = [set(c) for c in nx.cliques_containing_node(G, 2, cliques=self.cl)]
assert answer in (expected, list(reversed(expected)))
assert len(nx.cliques_containing_node(G)) == 11
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.project(B, range(1, 12))
assert H.adj == G.adj
# Project onto the nodes representing the cliques.
H1 = nx.project(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.project(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):
cliques = nx.find_cliques(nx.DiGraph())
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)))