242 lines
9.6 KiB
Python
242 lines
9.6 KiB
Python
#!/usr/bin/env python
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"""
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Threshold Graphs
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================
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"""
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import pytest
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import networkx as nx
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import networkx.algorithms.threshold as nxt
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from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic
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from networkx.testing import almost_equal
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cnlti = nx.convert_node_labels_to_integers
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class TestGeneratorThreshold():
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def test_threshold_sequence_graph_test(self):
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G = nx.star_graph(10)
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assert nxt.is_threshold_graph(G)
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assert nxt.is_threshold_sequence(list(d for n, d in G.degree()))
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G = nx.complete_graph(10)
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assert nxt.is_threshold_graph(G)
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assert nxt.is_threshold_sequence(list(d for n, d in G.degree()))
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deg = [3, 2, 2, 1, 1, 1]
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assert not nxt.is_threshold_sequence(deg)
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deg = [3, 2, 2, 1]
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assert nxt.is_threshold_sequence(deg)
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G = nx.generators.havel_hakimi_graph(deg)
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assert nxt.is_threshold_graph(G)
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def test_creation_sequences(self):
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deg = [3, 2, 2, 1]
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G = nx.generators.havel_hakimi_graph(deg)
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with pytest.raises(ValueError):
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nxt.creation_sequence(deg, with_labels=True, compact=True)
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cs0 = nxt.creation_sequence(deg)
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H0 = nxt.threshold_graph(cs0)
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assert ''.join(cs0) == 'ddid'
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cs1 = nxt.creation_sequence(deg, with_labels=True)
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H1 = nxt.threshold_graph(cs1)
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assert cs1 == [(1, 'd'), (2, 'd'), (3, 'i'), (0, 'd')]
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cs2 = nxt.creation_sequence(deg, compact=True)
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H2 = nxt.threshold_graph(cs2)
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assert cs2 == [2, 1, 1]
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assert ''.join(nxt.uncompact(cs2)) == 'ddid'
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assert graph_could_be_isomorphic(H0, G)
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assert graph_could_be_isomorphic(H0, H1)
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assert graph_could_be_isomorphic(H0, H2)
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def test_make_compact(self):
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assert nxt.make_compact(['d', 'd', 'd', 'i', 'd', 'd']) == [3, 1, 2]
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assert nxt.make_compact([3, 1, 2]) == [3, 1, 2]
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assert pytest.raises(TypeError, nxt.make_compact, [3., 1., 2.])
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def test_uncompact(self):
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assert nxt.uncompact([3, 1, 2]) == ['d', 'd', 'd', 'i', 'd', 'd']
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assert nxt.uncompact(['d', 'd', 'i', 'd']) == ['d', 'd', 'i', 'd']
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assert (nxt.uncompact(nxt.uncompact([(1, 'd'), (2, 'd'), (3, 'i'), (0, 'd')])) ==
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nxt.uncompact([(1, 'd'), (2, 'd'), (3, 'i'), (0, 'd')]))
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assert pytest.raises(TypeError, nxt.uncompact, [3., 1., 2.])
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def test_creation_sequence_to_weights(self):
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assert nxt.creation_sequence_to_weights([3, 1, 2]) == [0.5, 0.5, 0.5, 0.25, 0.75, 0.75]
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assert pytest.raises(TypeError, nxt.creation_sequence_to_weights, [3., 1., 2.])
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def test_weights_to_creation_sequence(self):
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deg = [3, 2, 2, 1]
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with pytest.raises(ValueError):
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nxt.weights_to_creation_sequence(deg, with_labels=True, compact=True)
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assert (nxt.weights_to_creation_sequence(deg, with_labels=True) ==
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[(3, 'd'), (1, 'd'), (2, 'd'), (0, 'd')])
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assert nxt.weights_to_creation_sequence(deg, compact=True) == [4]
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def test_find_alternating_4_cycle(self):
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G = nx.Graph()
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G.add_edge(1, 2)
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assert not nxt.find_alternating_4_cycle(G)
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def test_shortest_path(self):
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deg = [3, 2, 2, 1]
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G = nx.generators.havel_hakimi_graph(deg)
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cs1 = nxt.creation_sequence(deg, with_labels=True)
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for n, m in [(3, 0), (0, 3), (0, 2), (0, 1), (1, 3),
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(3, 1), (1, 2), (2, 3)]:
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assert (nxt.shortest_path(cs1, n, m) ==
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nx.shortest_path(G, n, m))
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spl = nxt.shortest_path_length(cs1, 3)
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spl2 = nxt.shortest_path_length([t for v, t in cs1], 2)
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assert spl == spl2
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spld = {}
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for j, pl in enumerate(spl):
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n = cs1[j][0]
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spld[n] = pl
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assert spld == nx.single_source_shortest_path_length(G, 3)
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assert nxt.shortest_path(['d', 'd', 'd', 'i', 'd', 'd'], 1, 2) == [1, 2]
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assert nxt.shortest_path([3, 1, 2], 1, 2) == [1, 2]
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assert pytest.raises(TypeError, nxt.shortest_path, [3., 1., 2.], 1, 2)
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assert pytest.raises(ValueError, nxt.shortest_path, [3, 1, 2], 'a', 2)
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assert pytest.raises(ValueError, nxt.shortest_path, [3, 1, 2], 1, 'b')
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assert nxt.shortest_path([3, 1, 2], 1, 1) == [1]
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def test_shortest_path_length(self):
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assert nxt.shortest_path_length([3, 1, 2], 1) == [1, 0, 1, 2, 1, 1]
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assert (nxt.shortest_path_length(['d', 'd', 'd', 'i', 'd', 'd'], 1) ==
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[1, 0, 1, 2, 1, 1])
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assert (nxt.shortest_path_length(('d', 'd', 'd', 'i', 'd', 'd'), 1) ==
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[1, 0, 1, 2, 1, 1])
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assert pytest.raises(TypeError, nxt.shortest_path, [3., 1., 2.], 1)
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def random_threshold_sequence(self):
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assert len(nxt.random_threshold_sequence(10, 0.5)) == 10
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assert (nxt.random_threshold_sequence(10, 0.5, seed=42) ==
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['d', 'i', 'd', 'd', 'd', 'i', 'i', 'i', 'd', 'd'])
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assert pytest.raises(ValueError, nxt.random_threshold_sequence, 10, 1.5)
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def test_right_d_threshold_sequence(self):
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assert nxt.right_d_threshold_sequence(3, 2) == ['d', 'i', 'd']
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assert pytest.raises(ValueError, nxt.right_d_threshold_sequence, 2, 3)
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def test_left_d_threshold_sequence(self):
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assert nxt.left_d_threshold_sequence(3, 2) == ['d', 'i', 'd']
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assert pytest.raises(ValueError, nxt.left_d_threshold_sequence, 2, 3)
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def test_weights_thresholds(self):
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wseq = [3, 4, 3, 3, 5, 6, 5, 4, 5, 6]
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cs = nxt.weights_to_creation_sequence(wseq, threshold=10)
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wseq = nxt.creation_sequence_to_weights(cs)
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cs2 = nxt.weights_to_creation_sequence(wseq)
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assert cs == cs2
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wseq = nxt.creation_sequence_to_weights(nxt.uncompact([3, 1, 2, 3, 3, 2, 3]))
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assert (wseq ==
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[s * 0.125 for s in [4, 4, 4, 3, 5, 5, 2, 2, 2, 6, 6, 6, 1, 1, 7, 7, 7]])
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wseq = nxt.creation_sequence_to_weights([3, 1, 2, 3, 3, 2, 3])
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assert (wseq ==
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[s * 0.125 for s in [4, 4, 4, 3, 5, 5, 2, 2, 2, 6, 6, 6, 1, 1, 7, 7, 7]])
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wseq = nxt.creation_sequence_to_weights(list(enumerate('ddidiiidididi')))
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assert (wseq ==
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[s * 0.1 for s in [5, 5, 4, 6, 3, 3, 3, 7, 2, 8, 1, 9, 0]])
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wseq = nxt.creation_sequence_to_weights('ddidiiidididi')
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assert (wseq ==
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[s * 0.1 for s in [5, 5, 4, 6, 3, 3, 3, 7, 2, 8, 1, 9, 0]])
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wseq = nxt.creation_sequence_to_weights('ddidiiidididid')
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ws = [s / float(12) for s in [6, 6, 5, 7, 4, 4, 4, 8, 3, 9, 2, 10, 1, 11]]
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assert sum([abs(c - d) for c, d in zip(wseq, ws)]) < 1e-14
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def test_finding_routines(self):
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G = nx.Graph({1: [2], 2: [3], 3: [4], 4: [5], 5: [6]})
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G.add_edge(2, 4)
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G.add_edge(2, 5)
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G.add_edge(2, 7)
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G.add_edge(3, 6)
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G.add_edge(4, 6)
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# Alternating 4 cycle
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assert nxt.find_alternating_4_cycle(G) == [1, 2, 3, 6]
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# Threshold graph
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TG = nxt.find_threshold_graph(G)
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assert nxt.is_threshold_graph(TG)
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assert sorted(TG.nodes()) == [1, 2, 3, 4, 5, 7]
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cs = nxt.creation_sequence(dict(TG.degree()), with_labels=True)
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assert nxt.find_creation_sequence(G) == cs
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def test_fast_versions_properties_threshold_graphs(self):
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cs = 'ddiiddid'
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G = nxt.threshold_graph(cs)
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assert nxt.density('ddiiddid') == nx.density(G)
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assert (sorted(nxt.degree_sequence(cs)) ==
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sorted(d for n, d in G.degree()))
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ts = nxt.triangle_sequence(cs)
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assert ts == list(nx.triangles(G).values())
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assert sum(ts) // 3 == nxt.triangles(cs)
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c1 = nxt.cluster_sequence(cs)
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c2 = list(nx.clustering(G).values())
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assert almost_equal(sum([abs(c - d) for c, d in zip(c1, c2)]), 0)
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b1 = nx.betweenness_centrality(G).values()
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b2 = nxt.betweenness_sequence(cs)
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assert sum([abs(c - d) for c, d in zip(b1, b2)]) < 1e-14
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assert nxt.eigenvalues(cs) == [0, 1, 3, 3, 5, 7, 7, 8]
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# Degree Correlation
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assert abs(nxt.degree_correlation(cs) + 0.593038821954) < 1e-12
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assert nxt.degree_correlation('diiiddi') == -0.8
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assert nxt.degree_correlation('did') == -1.0
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assert nxt.degree_correlation('ddd') == 1.0
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assert nxt.eigenvalues('dddiii') == [0, 0, 0, 0, 3, 3]
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assert nxt.eigenvalues('dddiiid') == [0, 1, 1, 1, 4, 4, 7]
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def test_tg_creation_routines(self):
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s = nxt.left_d_threshold_sequence(5, 7)
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s = nxt.right_d_threshold_sequence(5, 7)
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s1 = nxt.swap_d(s, 1.0, 1.0)
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s1 = nxt.swap_d(s, 1.0, 1.0, seed=1)
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def test_eigenvectors(self):
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np = pytest.importorskip('numpy')
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eigenval = np.linalg.eigvals
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scipy = pytest.importorskip('scipy')
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cs = 'ddiiddid'
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G = nxt.threshold_graph(cs)
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(tgeval, tgevec) = nxt.eigenvectors(cs)
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dot = np.dot
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assert [abs(dot(lv, lv) - 1.0) < 1e-9 for lv in tgevec] == [True] * 8
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lapl = nx.laplacian_matrix(G)
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# tgev=[ dot(lv,dot(lapl,lv)) for lv in tgevec ]
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# assert_true(sum([abs(c-d) for c,d in zip(tgev,tgeval)]) < 1e-9)
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# tgev.sort()
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# lev=list(eigenval(lapl))
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# lev.sort()
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# assert_true(sum([abs(c-d) for c,d in zip(tgev,lev)]) < 1e-9)
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def test_create_using(self):
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cs = 'ddiiddid'
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G = nxt.threshold_graph(cs)
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assert pytest.raises(nx.exception.NetworkXError,
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nxt.threshold_graph, cs, create_using=nx.DiGraph())
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MG = nxt.threshold_graph(cs, create_using=nx.MultiGraph())
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assert sorted(MG.edges()) == sorted(G.edges())
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