code: def paper_1_case(
      float_edge_wt=False, explicit_node_wt=True, directed=False
  ):
      # problem-specific constants
      limit = 3
  
      # configuration
      if float_edge_wt:
          shift = 0.001
      else:
          shift = 0
  
      if directed:
          example_1 = nx.DiGraph()
      else:
          example_1 = nx.Graph()
  
      # graph creation
      example_1.add_edge(1, 2, **{EWL: 3 + shift})
      example_1.add_edge(1, 4, **{EWL: 2 + shift})
      example_1.add_edge(2, 3, **{EWL: 4 + shift})
      example_1.add_edge(2, 5, **{EWL: 6 + shift})
  
      # node weights
      if explicit_node_wt:
          nx.set_node_attributes(example_1, 1, NWL)
          wtu = NWL
      else:
          wtu = None
  
      # partitioning
      clusters_1 = {
          frozenset(x)
          for x in nx.community.lukes_partitioning(
              example_1, limit, node_weight=wtu, edge_weight=EWL
          )
      }
  
      return clusters_1
  
file_path: networkx/networkx/algorithms/community/tests/test_lukes.py
imports: from itertools import product
  import pytest
  import networkx
label_desc: Use image node_id 1 for calling a global function with example usage: paper_1_case(float_edge_wt, explicit_node_wt, directed) and returns: clusters_1