code: def test_spectral_embedding_first_eigen_vector():
      # Test that the first eigenvector of spectral_embedding
      # is constant and that the second is not (for a connected graph)
      random_state = np.random.RandomState(36)
      data = random_state.randn(10, 30)
      sims = rbf_kernel(data)
      n_components = 2
  
      for seed in range(10):
          embedding = spectral_embedding(
              sims,
              norm_laplacian=False,
              n_components=n_components,
              drop_first=False,
              random_state=seed,
          )
  
          assert np.std(embedding[:, 0]) == pytest.approx(0)
          assert np.std(embedding[:, 1]) > 1e-3
  
imports: from unittest.mock import Mock
  import numpy
  import pytest
  from scipy import sparse
  from scipy.linalg import eigh
  from scipy.sparse.linalg import eigsh, lobpcg
  from sklearn.cluster import KMeans
  from sklearn.datasets import make_blobs
  from sklearn.manifold import SpectralEmbedding, _spectral_embedding, spectral_embedding
  from sklearn.manifold._spectral_embedding import _graph_connected_component, _graph_is_connected
  from sklearn.metrics import normalized_mutual_info_score, pairwise_distances
  from sklearn.metrics.pairwise import rbf_kernel
  from sklearn.neighbors import NearestNeighbors
  from sklearn.utils._testing import assert_array_almost_equal, assert_array_equal
  from sklearn.utils.extmath import _deterministic_vector_sign_flip
  from sklearn.utils.fixes import COO_CONTAINERS, CSC_CONTAINERS, CSR_CONTAINERS, parse_version, sp_version
  from sklearn.utils.fixes import laplacian
label_desc: Use image node_id 13 for calling a global function with example usage: test_spectral_embedding_first_eigen_vector() without return types