content: import numpy as np
  import scipy.sparse as sp
  
  
  def sparse_to_tuple(sparse_mx):
      if not sp.isspmatrix_coo(sparse_mx):
          sparse_mx = sparse_mx.tocoo()
      coords = np.vstack((sparse_mx.row, sparse_mx.col)).transpose()
      values = sparse_mx.data
      shape = sparse_mx.shape
      return coords, values, shape
  
  
  def preprocess_graph(adj):
      adj = sp.coo_matrix(adj)
      adj_ = adj + sp.eye(adj.shape[0])
      rowsum = np.array(adj_.sum(1))
      degree_mat_inv_sqrt = sp.diags(np.power(rowsum, -0.5).flatten())
      adj_normalized = adj_.dot(degree_mat_inv_sqrt).transpose().dot(degree_mat_inv_sqrt).tocoo()
      return sparse_to_tuple(adj_normalized)
  
  
  def construct_feed_dict(adj_normalized, adj, features, placeholders):
      # construct feed dictionary
      feed_dict = dict()
      feed_dict.update({placeholders['features']: features})
      feed_dict.update({placeholders['adj']: adj_normalized})
      feed_dict.update({placeholders['adj_orig']: adj})
      return feed_dict
  
  
  def mask_test_edges(adj):
      # Function to build test set with 10% positive links
      # NOTE: Splits are randomized and results might slightly deviate from reported numbers in the paper.
      # TODO: Clean up.
  
      # Remove diagonal elements
      adj = adj - sp.dia_matrix((adj.diagonal()[np.newaxis, :], [0]), shape=adj.shape)
      adj.eliminate_zeros()
      # Check that diag is zero:
      assert np.diag(adj.todense()).sum() == 0
  
      adj_triu = sp.triu(adj)
      adj_tuple = sparse_to_tuple(adj_triu)
      edges = adj_tuple[0]
      edges_all = sparse_to_tuple(adj)[0]
      num_test = int(np.floor(edges.shape[0] / 10.))
      num_val = int(np.floor(edges.shape[0] / 20.))
  
      all_edge_idx = list(range(edges.shape[0]))
      np.random.shuffle(all_edge_idx)
      val_edge_idx = all_edge_idx[:num_val]
      test_edge_idx = all_edge_idx[num_val:(num_val + num_test)]
      test_edges = edges[test_edge_idx]
      val_edges = edges[val_edge_idx]
      train_edges = np.delete(edges, np.hstack([test_edge_idx, val_edge_idx]), axis=0)
  
      def ismember(a, b, tol=5):
          rows_close = np.all(np.round(a - b[:, None], tol) == 0, axis=-1)
          return np.any(rows_close)
  
      test_edges_false = []
      while len(test_edges_false) < len(test_edges):
          idx_i = np.random.randint(0, adj.shape[0])
          idx_j = np.random.randint(0, adj.shape[0])
          if idx_i == idx_j:
              continue
          if ismember([idx_i, idx_j], edges_all):
              continue
          if test_edges_false:
              if ismember([idx_j, idx_i], np.array(test_edges_false)):
                  continue
              if ismember([idx_i, idx_j], np.array(test_edges_false)):
                  continue
          test_edges_false.append([idx_i, idx_j])
  
      val_edges_false = []
      while len(val_edges_false) < len(val_edges):
          idx_i = np.random.randint(0, adj.shape[0])
          idx_j = np.random.randint(0, adj.shape[0])
          if idx_i == idx_j:
              continue
          if ismember([idx_i, idx_j], train_edges):
              continue
          if ismember([idx_j, idx_i], train_edges):
              continue
          if ismember([idx_i, idx_j], val_edges):
              continue
          if ismember([idx_j, idx_i], val_edges):
              continue
          if val_edges_false:
              if ismember([idx_j, idx_i], np.array(val_edges_false)):
                  continue
              if ismember([idx_i, idx_j], np.array(val_edges_false)):
                  continue
          val_edges_false.append([idx_i, idx_j])
  
      assert ~ismember(test_edges_false, edges_all)
      assert ~ismember(val_edges_false, edges_all)
      assert ~ismember(val_edges, train_edges)
      assert ~ismember(test_edges, train_edges)
      assert ~ismember(val_edges, test_edges)
  
      data = np.ones(train_edges.shape[0])
  
      # Re-build adj matrix
      adj_train = sp.csr_matrix((data, (train_edges[:, 0], train_edges[:, 1])), shape=adj.shape)
      adj_train = adj_train + adj_train.T
  
      # NOTE: these edge lists only contain single direction of edge!
      return adj_train, train_edges, val_edges, val_edges_false, test_edges, test_edges_false
  