code: def test_v_measure_and_mutual_information(seed=36):
      # Check relation between v_measure, entropy and mutual information
      for i in np.logspace(1, 4, 4).astype(int):
          random_state = np.random.RandomState(seed)
          labels_a, labels_b = (
              random_state.randint(0, 10, i),
              random_state.randint(0, 10, i),
          )
          assert_almost_equal(
              v_measure_score(labels_a, labels_b),
              2.0
              * mutual_info_score(labels_a, labels_b)
              / (entropy(labels_a) + entropy(labels_b)),
              0,
          )
          avg = "arithmetic"
          assert_almost_equal(
              v_measure_score(labels_a, labels_b),
              normalized_mutual_info_score(
                  labels_a, labels_b, average_method=avg
              ),
          )
  
imports: import warnings
  import numpy
  import pytest
  from numpy.testing import assert_allclose, assert_array_almost_equal, assert_array_equal
  from sklearn.metrics.cluster import adjusted_mutual_info_score, adjusted_rand_score, completeness_score, contingency_matrix, entropy, expected_mutual_information, fowlkes_mallows_score, homogeneity_completeness_v_measure, homogeneity_score, mutual_info_score, normalized_mutual_info_score, pair_confusion_matrix, rand_score, v_measure_score
  from sklearn.metrics.cluster._supervised import _generalized_average, check_clusterings
  from sklearn.utils import assert_all_finite
  from sklearn.utils._testing import assert_almost_equal
label_desc: Use image node_id 18 for calling a global function with example usage: test_v_measure_and_mutual_information(seed) without return types