text: """
  Threshold Graphs
  ================
  """
  
  import pytest
  
  import networkx as nx
  import networkx.algorithms.threshold as nxt
  from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic
  from networkx.testing import almost_equal
  
  cnlti = nx.convert_node_labels_to_integers
  
  
  class TestGeneratorThreshold():
      def test_threshold_sequence_graph_test(self):
          G = nx.star_graph(10)
          assert nxt.is_threshold_graph(G)
          assert nxt.is_threshold_sequence(list(d for n, d in G.degree()))
  
          G = nx.complete_graph(10)
          assert nxt.is_threshold_graph(G)
          assert nxt.is_threshold_sequence(list(d for n, d in G.degree()))
  
          deg = [3, 2, 2, 1, 1, 1]
          assert not nxt.is_threshold_sequence(deg)
  
          deg = [3, 2, 2, 1]
          assert nxt.is_threshold_sequence(deg)
  
          G = nx.generators.havel_hakimi_graph(deg)
          assert nxt.is_threshold_graph(G)
  
      def test_creation_sequences(self):
          deg = [3, 2, 2, 1]
          G = nx.generators.havel_hakimi_graph(deg)
  
          with pytest.raises(ValueError):
              nxt.creation_sequence(deg, with_labels=True, compact=True)
  
          cs0 = nxt.creation_sequence(deg)
          H0 = nxt.threshold_graph(cs0)
          assert ''.join(cs0) == 'ddid'
  
          cs1 = nxt.creation_sequence(deg, with_labels=True)
          H1 = nxt.threshold_graph(cs1)
          assert cs1 == [(1, 'd'), (2, 'd'), (3, 'i'), (0, 'd')]
  
          cs2 = nxt.creation_sequence(deg, compact=True)
          H2 = nxt.threshold_graph(cs2)
          assert cs2 == [2, 1, 1]
          assert ''.join(nxt.uncompact(cs2)) == 'ddid'
          assert graph_could_be_isomorphic(H0, G)
          assert graph_could_be_isomorphic(H0, H1)
          assert graph_could_be_isomorphic(H0, H2)
  
      def test_make_compact(self):
          assert nxt.make_compact(['d', 'd', 'd', 'i', 'd', 'd']) == [3, 1, 2]
          assert nxt.make_compact([3, 1, 2]) == [3, 1, 2]
          assert pytest.raises(TypeError, nxt.make_compact, [3., 1., 2.])
  
      def test_uncompact(self):
          assert nxt.uncompact([3, 1, 2]) == ['d', 'd', 'd', 'i', 'd', 'd']
          assert nxt.uncompact(['d', 'd', 'i', 'd']) == ['d', 'd', 'i', 'd']
          assert (nxt.uncompact(nxt.uncompact([(1, 'd'), (2, 'd'), (3, 'i'), (0, 'd')])) ==
                  nxt.uncompact([(1, 'd'), (2, 'd'), (3, 'i'), (0, 'd')]))
          assert pytest.raises(TypeError, nxt.uncompact, [3., 1., 2.])
  
      def test_creation_sequence_to_weights(self):
          assert nxt.creation_sequence_to_weights([3, 1, 2]) == [0.5, 0.5, 0.5, 0.25, 0.75, 0.75]
          assert pytest.raises(TypeError, nxt.creation_sequence_to_weights, [3., 1., 2.])
  
      def test_weights_to_creation_sequence(self):
          deg = [3, 2, 2, 1]
          with pytest.raises(ValueError):
              nxt.weights_to_creation_sequence(deg, with_labels=True, compact=True)
          assert (nxt.weights_to_creation_sequence(deg, with_labels=True) ==
                  [(3, 'd'), (1, 'd'), (2, 'd'), (0, 'd')])
          assert 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 not 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 (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 spl == spl2
  
          spld = {}
          for j, pl in enumerate(spl):
              n = cs1[j][0]
              spld[n] = pl
          assert spld == nx.single_source_shortest_path_length(G, 3)
  
          assert nxt.shortest_path(['d', 'd', 'd', 'i', 'd', 'd'], 1, 2) == [1, 2]
          assert nxt.shortest_path([3, 1, 2], 1, 2) == [1, 2]
          assert pytest.raises(TypeError, nxt.shortest_path, [3., 1., 2.], 1, 2)
          assert pytest.raises(ValueError, nxt.shortest_path, [3, 1, 2], 'a', 2)
          assert pytest.raises(ValueError, nxt.shortest_path, [3, 1, 2], 1, 'b')
          assert nxt.shortest_path([3, 1, 2], 1, 1) == [1]
  
      def test_shortest_path_length(self):
          assert nxt.shortest_path_length([3, 1, 2], 1) == [1, 0, 1, 2, 1, 1]
          assert (nxt.shortest_path_length(['d', 'd', 'd', 'i', 'd', 'd'], 1) ==
                  [1, 0, 1, 2, 1, 1])
          assert (nxt.shortest_path_length(('d', 'd', 'd', 'i', 'd', 'd'), 1) ==
                  [1, 0, 1, 2, 1, 1])
          assert pytest.raises(TypeError, nxt.shortest_path, [3., 1., 2.], 1)
  
      def random_threshold_sequence(self):
          assert len(nxt.random_threshold_sequence(10, 0.5)) == 10
          assert (nxt.random_threshold_sequence(10, 0.5, seed=42) ==
                  ['d', 'i', 'd', 'd', 'd', 'i', 'i', 'i', 'd', 'd'])
          assert pytest.raises(ValueError, nxt.random_threshold_sequence, 10, 1.5)
  
      def test_right_d_threshold_sequence(self):
          assert nxt.right_d_threshold_sequence(3, 2) == ['d', 'i', 'd']
          assert pytest.raises(ValueError, nxt.right_d_threshold_sequence, 2, 3)
  
      def test_left_d_threshold_sequence(self):
          assert nxt.left_d_threshold_sequence(3, 2) == ['d', 'i', 'd']
          assert pytest.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 cs == cs2
  
          wseq = nxt.creation_sequence_to_weights(nxt.uncompact([3, 1, 2, 3, 3, 2, 3]))
          assert (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 (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 (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 (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 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 nxt.find_alternating_4_cycle(G) == [1, 2, 3, 6]
  
          # Threshold graph
          TG = nxt.find_threshold_graph(G)
          assert nxt.is_threshold_graph(TG)
          assert sorted(TG.nodes()) == [1, 2, 3, 4, 5, 7]
  
          cs = nxt.creation_sequence(dict(TG.degree()), with_labels=True)
          assert nxt.find_creation_sequence(G) == cs
  
      def test_fast_versions_properties_threshold_graphs(self):
          cs = 'ddiiddid'
          G = nxt.threshold_graph(cs)
          assert nxt.density('ddiiddid') == nx.density(G)
          assert (sorted(nxt.degree_sequence(cs)) ==
                  sorted(d for n, d in G.degree()))
  
          ts = nxt.triangle_sequence(cs)
          assert ts == list(nx.triangles(G).values())
          assert 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 sum([abs(c - d) for c, d in zip(b1, b2)]) < 1e-14
  
          assert nxt.eigenvalues(cs) == [0, 1, 3, 3, 5, 7, 7, 8]
  
          # Degree Correlation
          assert abs(nxt.degree_correlation(cs) + 0.593038821954) < 1e-12
          assert nxt.degree_correlation('diiiddi') == -0.8
          assert nxt.degree_correlation('did') == -1.0
          assert nxt.degree_correlation('ddd') == 1.0
          assert nxt.eigenvalues('dddiii') == [0, 0, 0, 0, 3, 3]
          assert 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)
          s1 = nxt.swap_d(s, 1.0, 1.0, seed=1)
  
      def test_eigenvectors(self):
          np = pytest.importorskip('numpy')
          eigenval = np.linalg.eigvals
          scipy = pytest.importorskip('scipy')
  
          cs = 'ddiiddid'
          G = nxt.threshold_graph(cs)
          (tgeval, tgevec) = nxt.eigenvectors(cs)
          dot = np.dot
          assert [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 pytest.raises(nx.exception.NetworkXError,
                               nxt.threshold_graph, cs, create_using=nx.DiGraph())
          MG = nxt.threshold_graph(cs, create_using=nx.MultiGraph())
          assert sorted(MG.edges()) == sorted(G.edges())
  