code: def test_ramsey():
      # this should only find the complete graph
      graph = nx.complete_graph(10)
      c, i = apxa.ramsey_R2(graph)
      cdens = nx.density(graph.subgraph(c))
      assert cdens == 1.0, "clique not correctly found by ramsey!"
      idens = nx.density(graph.subgraph(i))
      assert idens == 0.0, "i-set not correctly found by ramsey!"
  
      # this trivial graph has no cliques. should just find i-sets
      graph = nx.trivial_graph()
      c, i = apxa.ramsey_R2(graph)
      assert c == {0}, "clique not correctly found by ramsey!"
      assert i == {0}, "i-set not correctly found by ramsey!"
  
      graph = nx.barbell_graph(10, 5, nx.Graph())
      c, i = apxa.ramsey_R2(graph)
      cdens = nx.density(graph.subgraph(c))
      assert cdens == 1.0, "clique not correctly found by ramsey!"
      idens = nx.density(graph.subgraph(i))
      assert idens == 0.0, "i-set not correctly found by ramsey!"
  
      # add self-loops and test again
      graph.add_edges_from([(n, n) for n in range(0, len(graph), 2)])
      cc, ii = apxa.ramsey_R2(graph)
      assert cc == c
      assert ii == i
  
label_desc: Use image node_id 1 for calling a global function with example usage: test_ramsey() without return types