def perturbed_mst(X, num_perturbations=20, metric='euclidean', jitter=None):
  '''Builds a graph as the union of several MSTs on perturbed data.
  Reference: http://ecovision.mit.edu/~sloop/shao.pdf, page 8
  jitter refers to the scale of the gaussian noise added for each perturbation.
  When jitter is None, it defaults to the 5th percentile interpoint distance.
  Note that metric cannot be 'precomputed', as multiple MSTs are computed.'''
  assert metric != 'precomputed'
  D = pairwise_distances(X, metric=metric)
  if jitter is None:
    jitter = np.percentile(D[D>0], 5)
  W = minimum_spanning_tree(D)
  W = W + W.T
  W.data[:] = 1.0  # binarize
  for i in range(num_perturbations):
    pX = X + np.random.normal(scale=jitter, size=X.shape)
    pW = minimum_spanning_tree(pairwise_distances(pX, metric=metric))
    pW = pW + pW.T
    pW.data[:] = 1.0
    W = W + pW
  # final graph is the average over all pertubed MSTs + the original
  W.data /= (num_perturbations + 1.0)
  return Graph.from_adj_matrix(W)