text: # Copyright (c) 2019-2021, NVIDIA CORPORATION.
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  
  from cugraph.structure.graph_classes import Graph
  from cugraph.link_prediction import jaccard_wrapper
  import cudf
  import numpy as np
  from cugraph.utilities import renumber_vertex_pair
  
  
  def jaccard_w(input_graph, weights, vertex_pair=None):
      """
      Compute the weighted Jaccard similarity between each pair of vertices
      connected by an edge, or between arbitrary pairs of vertices specified by
      the user. Jaccard similarity is defined between two sets as the ratio of
      the volume of their intersection divided by the volume of their union. In
      the context of graphs, the neighborhood of a vertex is seen as a set. The
      Jaccard similarity weight of each edge represents the strength of
      connection between vertices based on the relative similarity of their
      neighbors. If first is specified but second is not, or vice versa, an
      exception will be thrown.
  
      Parameters
      ----------
      graph : cugraph.Graph
          cuGraph graph descriptor, should contain the connectivity information
          as an edge list (edge weights are not used for this algorithm). The
          adjacency list will be computed if not already present.
  
      weights : cudf.DataFrame
          Specifies the weights to be used for each vertex.
          Vertex should be represented by multiple columns for multi-column
          vertices.
  
          weights['vertex'] : cudf.Series
              Contains the vertex identifiers
          weights['weight'] : cudf.Series
              Contains the weights of vertices
  
      vertex_pair : cudf.DataFrame
          A GPU dataframe consisting of two columns representing pairs of
          vertices. If provided, the jaccard coefficient is computed for the
          given vertex pairs, else, it is computed for all vertex pairs.
  
      Returns
      -------
      df : cudf.DataFrame
          GPU data frame of size E (the default) or the size of the given pairs
          (first, second) containing the Jaccard weights. The ordering is
          relative to the adjacency list, or that given by the specified vertex
          pairs.
  
          df['source'] : cudf.Series
              The source vertex ID
          df['destination'] : cudf.Series
              The destination vertex ID
          df['jaccard_coeff'] : cudf.Series
              The computed weighted Jaccard coefficient between the source and
              destination vertices.
  
      Examples
      --------
      >>> M = cudf.read_csv('datasets/karate.csv', delimiter=' ',
      >>>                   dtype=['int32', 'int32', 'float32'], header=None)
      >>> G = cugraph.Graph()
      >>> G.from_cudf_edgelist(M, source='0', destination='1')
      >>> df = cugraph.jaccard_w(G, M[2])
      """
      if type(input_graph) is not Graph:
          raise Exception("input graph must be undirected")
  
      if type(vertex_pair) == cudf.DataFrame:
          vertex_pair = renumber_vertex_pair(input_graph, vertex_pair)
      elif vertex_pair is None:
          pass
      else:
          raise ValueError("vertex_pair must be a cudf dataframe")
  
      if input_graph.renumbered:
          vertex_size = input_graph.vertex_column_size()
          if vertex_size == 1:
              weights = input_graph.add_internal_vertex_id(
                  weights, 'vertex', 'vertex'
              )
          else:
              cols = weights.columns[:vertex_size].to_list()
              weights = input_graph.add_internal_vertex_id(
                  weights, 'vertex', cols
              )
      jaccard_weights = cudf.Series(np.ones(len(weights)))
      for i in range(len(weights)):
          jaccard_weights[weights['vertex'].iloc[i]] = weights['weight'].iloc[i]
      df = jaccard_wrapper.jaccard(input_graph, jaccard_weights, vertex_pair)
  
      if input_graph.renumbered:
          df = input_graph.unrenumber(df, "source")
          df = input_graph.unrenumber(df, "destination")
  
      return df
  