text: #!/usr/bin/env python
  import random
  
  import networkx
  import pytest
  import pytest
  numpy = pytest.importorskip('numpy')
  scipy = pytest.importorskip('scipy')
  
  from networkx.testing import almost_equal
  
  # Example from
  # A. Langville and C. Meyer, "A survey of eigenvector methods of web
  # information retrieval."  http://citeseer.ist.psu.edu/713792.html
  
  
  class TestPageRank(object):
  
      @classmethod
      def setup_class(cls):
          G = networkx.DiGraph()
          edges = [(1, 2), (1, 3),
                   # 2 is a dangling node
                   (3, 1), (3, 2), (3, 5),
                   (4, 5), (4, 6),
                   (5, 4), (5, 6),
                   (6, 4)]
          G.add_edges_from(edges)
          cls.G = G
          cls.G.pagerank = dict(zip(sorted(G),
                                     [0.03721197, 0.05395735, 0.04150565,
                                      0.37508082, 0.20599833, 0.28624589]))
          cls.dangling_node_index = 1
          cls.dangling_edges = {1: 2, 2: 3,
                                 3: 0, 4: 0, 5: 0, 6: 0}
          cls.G.dangling_pagerank = dict(zip(sorted(G),
                                              [0.10844518, 0.18618601, 0.0710892,
                                               0.2683668, 0.15919783, 0.20671497]))
  
      def test_pagerank(self):
          G = self.G
          p = networkx.pagerank(G, alpha=0.9, tol=1.e-08)
          for n in G:
              assert almost_equal(p[n], G.pagerank[n], places=4)
  
          nstart = dict((n, random.random()) for n in G)
          p = networkx.pagerank(G, alpha=0.9, tol=1.e-08, nstart=nstart)
          for n in G:
              assert almost_equal(p[n], G.pagerank[n], places=4)
  
      def test_pagerank_max_iter(self):
          with pytest.raises(networkx.PowerIterationFailedConvergence):
              networkx.pagerank(self.G, max_iter=0)
  
      def test_numpy_pagerank(self):
          G = self.G
          p = networkx.pagerank_numpy(G, alpha=0.9)
          for n in G:
              assert almost_equal(p[n], G.pagerank[n], places=4)
          personalize = dict((n, random.random()) for n in G)
          p = networkx.pagerank_numpy(G, alpha=0.9, personalization=personalize)
  
      def test_google_matrix(self):
          G = self.G
          M = networkx.google_matrix(G, alpha=0.9, nodelist=sorted(G))
          e, ev = numpy.linalg.eig(M.T)
          p = numpy.array(ev[:, 0] / ev[:, 0].sum())[:, 0]
          for (a, b) in zip(p, self.G.pagerank.values()):
              assert almost_equal(a, b)
  
      def test_personalization(self):
          G = networkx.complete_graph(4)
          personalize = {0: 1, 1: 1, 2: 4, 3: 4}
          answer = {0: 0.23246732615667579, 1: 0.23246732615667579, 2: 0.267532673843324, 3: 0.2675326738433241}
          p = networkx.pagerank(G, alpha=0.85, personalization=personalize)
          for n in G:
              assert almost_equal(p[n], answer[n], places=4)
  
      def test_zero_personalization_vector(self):
          G = networkx.complete_graph(4)
          personalize = {0: 0, 1: 0, 2: 0, 3: 0}
          pytest.raises(ZeroDivisionError, networkx.pagerank, G,
                        personalization=personalize)
  
      def test_one_nonzero_personalization_value(self):
          G = networkx.complete_graph(4)
          personalize = {0: 0, 1: 0, 2: 0, 3: 1}
          answer = {0: 0.22077931820379187, 1: 0.22077931820379187, 2: 0.22077931820379187, 3: 0.3376620453886241}
          p = networkx.pagerank(G, alpha=0.85, personalization=personalize)
          for n in G:
              assert almost_equal(p[n], answer[n], places=4)
  
      def test_incomplete_personalization(self):
          G = networkx.complete_graph(4)
          personalize = {3: 1}
          answer = {0: 0.22077931820379187, 1: 0.22077931820379187, 2: 0.22077931820379187, 3: 0.3376620453886241}
          p = networkx.pagerank(G, alpha=0.85, personalization=personalize)
          for n in G:
              assert almost_equal(p[n], answer[n], places=4)
  
      def test_dangling_matrix(self):
          """
          Tests that the google_matrix doesn't change except for the dangling
          nodes.
          """
          G = self.G
          dangling = self.dangling_edges
          dangling_sum = float(sum(dangling.values()))
          M1 = networkx.google_matrix(G, personalization=dangling)
          M2 = networkx.google_matrix(G, personalization=dangling,
                                      dangling=dangling)
          for i in range(len(G)):
              for j in range(len(G)):
                  if i == self.dangling_node_index and (j + 1) in dangling:
                      assert almost_equal(M2[i, j],
                                          dangling[j + 1] / dangling_sum,
                                          places=4)
                  else:
                      assert almost_equal(M2[i, j], M1[i, j], places=4)
  
      def test_dangling_pagerank(self):
          pr = networkx.pagerank(self.G, dangling=self.dangling_edges)
          for n in self.G:
              assert almost_equal(pr[n], self.G.dangling_pagerank[n], places=4)
  
      def test_dangling_numpy_pagerank(self):
          pr = networkx.pagerank_numpy(self.G, dangling=self.dangling_edges)
          for n in self.G:
              assert almost_equal(pr[n], self.G.dangling_pagerank[n], places=4)
  
      def test_empty(self):
          G = networkx.Graph()
          assert networkx.pagerank(G) == {}
          assert networkx.pagerank_numpy(G) == {}
          assert networkx.google_matrix(G).shape == (0, 0)
  
  
  class TestPageRankScipy(TestPageRank):
  
      def test_scipy_pagerank(self):
          G = self.G
          p = networkx.pagerank_scipy(G, alpha=0.9, tol=1.e-08)
          for n in G:
              assert almost_equal(p[n], G.pagerank[n], places=4)
          personalize = dict((n, random.random()) for n in G)
          p = networkx.pagerank_scipy(G, alpha=0.9, tol=1.e-08,
                                      personalization=personalize)
  
          nstart = dict((n, random.random()) for n in G)
          p = networkx.pagerank_scipy(G, alpha=0.9, tol=1.e-08, nstart=nstart)
          for n in G:
              assert almost_equal(p[n], G.pagerank[n], places=4)
  
      def test_scipy_pagerank_max_iter(self):
          with pytest.raises(networkx.PowerIterationFailedConvergence):
              networkx.pagerank_scipy(self.G, max_iter=0)
  
      def test_dangling_scipy_pagerank(self):
          pr = networkx.pagerank_scipy(self.G, dangling=self.dangling_edges)
          for n in self.G:
              assert almost_equal(pr[n], self.G.dangling_pagerank[n], places=4)
  
      def test_empty_scipy(self):
          G = networkx.Graph()
          assert networkx.pagerank_scipy(G) == {}
  