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