<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:

def _prune_edges(G, X, traj_lengths, pruning_thresh=0.1, verbose=False):
  '''Prune edges in graph G via cosine distance with trajectory edges.'''
  W = G.matrix('dense', copy=True)
  degree = G.degree(kind='out', weighted=False)
  i = 0
  num_bad = 0
  for n in traj_lengths:
    s, t = np.nonzero(W[i:i+n-1])
    graph_edges = X[t] - X[s+i]
    traj_edges = np.diff(X[i:i+n], axis=0)
    traj_edges = np.repeat(traj_edges, degree[i:i+n-1], axis=0)
    theta = paired_distances(graph_edges, traj_edges, 'cosine')
    bad_edges = theta > pruning_thresh
    s, t = s[bad_edges], t[bad_edges]
    if verbose:  # pragma: no cover
      num_bad += np.count_nonzero(W[s,t])
    W[s,t] = 0
    i += n
  if verbose:  # pragma: no cover
    print('removed %d bad edges' % num_bad)
  return Graph.from_adj_matrix(W)