code: def louvain(
      G: Union[Graph, "networkx.Graph"],
      max_level: Union[int, None] = None,
      max_iter: Union[int, None] = None,
      resolution: float = 1.0,
      threshold: float = 1e-7,
  ) -> Tuple[Union[cudf.DataFrame, dict], float]:
      """
      Compute the modularity optimizing partition of the input graph using the
      Louvain method
  
      It uses the Louvain method described in:
  
      VD Blondel, J-L Guillaume, R Lambiotte and E Lefebvre: Fast unfolding of
      community hierarchies in large networks, J Stat Mech P10008 (2008),
      http://arxiv.org/abs/0803.0476
  
      Parameters
      ----------
      G : cugraph.Graph or NetworkX Graph
          The graph descriptor should contain the connectivity information
          and weights. The adjacency list will be computed if not already
          present.
          The current implementation only supports undirected graphs.
  
      max_level : integer, optional (default=100)
          This controls the maximum number of levels of the Louvain
          algorithm. When specified the algorithm will terminate after no more
          than the specified number of levels. No error occurs when the
          algorithm terminates early in this manner.
  
          If max_level > 500, it will be set to 500 and a warning is emitted
          in order to prevent excessive runtime.
  
      max_iter : integer, optional (default=None)
          This parameter is deprecated in favor of max_level.  Previously
          it was used to control the maximum number of levels of the Louvain
          algorithm.
  
      resolution: float, optional (default=1.0)
          Called gamma in the modularity formula, this changes the size
          of the communities.  Higher resolutions lead to more smaller
          communities, lower resolutions lead to fewer larger communities.
          Defaults to 1.
  
      threshold: float
          Modularity gain threshold for each level. If the gain of
          modularity between 2 levels of the algorithm is less than the
          given threshold then the algorithm stops and returns the
          resulting communities.
          Defaults to 1e-7.
  
      Returns
      -------
      result: cudf.DataFrame or dict
          If input graph G is of type cugraph.Graph, a GPU dataframe
          with two columns.
  
              result[VERTEX_COL_NAME] : cudf.Series
                  Contains the vertex identifiers
              result[CLUSTER_ID_COL_NAME] : cudf.Series
                  Contains the partition assigned to the vertices
  
          If input graph G is of type networkx.Graph, a dict
          Dictionary of vertices and their partition ids.
  
      modularity_score : float
          A floating point number containing the global modularity score
          of the partitioning.
  
      Examples
      --------
      >>> from cugraph.datasets import karate
      >>> G = karate.get_graph(download=True)
      >>> parts = cugraph.louvain(G)
  
      """
  
      # FIXME: Onece the graph construction calls support isolated vertices through
      #  the C API (the C++ interface already supports this) then there will be
      # no need to compute isolated vertices here.
  
      isolated_vertices = list()
      if is_nx_graph_type(type(G)):
          isolated_vertices = [
              v for v in range(G.number_of_nodes()) if G.degree[v] == 0
          ]
      else:
          # FIXME: Gather isolated vertices of G
          pass
  
      G, isNx = ensure_cugraph_obj_for_nx(G)
  
      if G.is_directed():
          raise ValueError("input graph must be undirected")
  
      # FIXME: This max_iter logic and the max_level defaulting can be deleted
      #        in favor of defaulting max_level in call once max_iter is deleted
      if max_iter:
          if max_level:
              raise ValueError(
                  "max_iter is deprecated.  Cannot specify both max_iter and max_level"
              )
  
          warning_msg = (
              "max_iter has been renamed max_level.  Use of max_iter is "
              "deprecated and will no longer be supported in the next releases."
          )
          warnings.warn(warning_msg, FutureWarning)
          max_level = max_iter
  
      if max_level is None:
          max_level = 100
  
      if max_level > 500:
          w_msg = "max_level is set too high, clamping it down to 500."
          warnings.warn(w_msg)
          max_level = 500
  
      vertex, partition, modularity_score = pylibcugraph_louvain(
          resource_handle=ResourceHandle(),
          graph=G._plc_graph,
          max_level=max_level,
          threshold=threshold,
          resolution=resolution,
          do_expensive_check=False,
      )
  
      result = cudf.DataFrame()
      result[VERTEX_COL_NAME] = vertex
      result[CLUSTER_ID_COL_NAME] = partition
  
      if len(isolated_vertices) > 0:
          unique_cids = result[CLUSTER_ID_COL_NAME].unique()
          max_cluster_id = -1 if len(result) == 0 else unique_cids.max()
  
          isolated_vtx_and_cids = cudf.DataFrame()
          isolated_vtx_and_cids[VERTEX_COL_NAME] = isolated_vertices
          isolated_vtx_and_cids[CLUSTER_ID_COL_NAME] = [
              (max_cluster_id + i + 1)
              for i in range(len(isolated_vertices))
          ]
          result = cudf.concat(
              [result, isolated_vtx_and_cids],
              ignore_index=True,
              sort=False,
          )
  
      if G.renumbered and len(G.input_df) > 0:
          result = G.unrenumber(result, VERTEX_COL_NAME)
  
      if isNx is True:
          result = df_score_to_dictionary(result, CLUSTER_ID_COL_NAME)
  
      return result, modularity_score
  
file_path: cugraph/python/cugraph/cugraph/community/louvain.py
imports: from typing import Union, Tuple
  from cugraph.structure import Graph
  from cugraph.utilities import is_nx_graph_type, ensure_cugraph_obj_for_nx, df_score_to_dictionary
  import cudf
  import warnings
  from pylibcugraph import louvain
  from pylibcugraph import ResourceHandle
  from cugraph.utilities.utils import import_optional
label_desc: Use image node_id 1 for calling a global function with example usage: louvain(G, max_level, max_iter, resolution, threshold) and returns: result,  modularity_score