code: def random_unlabeled_rooted_forest(
      n, *, q=None, number_of_forests=None, seed=None
  ):
      """Returns a forest or list of forests selected at random.
  
      Returns one or more (depending on `number_of_forests`)
      unlabeled rooted forests with `n` nodes, and with no more than
      `q` nodes per tree, drawn uniformly at random.
      The "roots" graph attribute identifies the roots of the forest.
  
      Parameters
      ----------
      n : int
          The number of nodes
      q : int or None (default)
          The maximum number of nodes per tree.
      number_of_forests : int or None (default)
          If not None, this number of forests is generated and returned.
      seed : integer, random_state, or None (default)
          Indicator of random number generation state.
          See :ref:`Randomness<randomness>`.
  
      Returns
      -------
      :class:`networkx.Graph` or list of :class:`networkx.Graph`
          A single `networkx.Graph` (or a list thereof, if `number_of_forests`
          is specified) with nodes in the set {0, …, *n* - 1}.
          The "roots" graph attribute is a set containing the roots
          of the trees in the forest.
  
      Notes
      -----
      This function implements the algorithm "Forest" of [1]_.
      The algorithm needs to compute some counting functions
      that are relatively expensive: in case several trees are needed,
      it is advisable to use the `number_of_forests` optional argument
      to reuse the counting functions.
  
      Raises
      ------
      ValueError
          If `n` is non-zero but `q` is zero.
  
      References
      ----------
      .. [1] Wilf, Herbert S. "The uniform selection of free trees."
          Journal of Algorithms 2.2 (1981): 204-207.
          https://doi.org/10.1016/0196-6774(81)90021-3
      """
      if q is None:
          q = n
      if q == 0 and n != 0:
          raise ValueError(
              "q must be a positive integer if n is positive."
          )
  
      cache_trees = [0, 1]  # initial cache of number of rooted trees
      cache_forests = [1]  # initial cache of number of rooted forests
  
      if number_of_forests is None:
          g, nodes, rs = _random_unlabeled_rooted_forest(
              n, q, cache_trees, cache_forests, seed
          )
          return _to_nx(g, nodes, roots=set(rs))
  
      res = []
      for i in range(number_of_forests):
          g, nodes, rs = _random_unlabeled_rooted_forest(
              n, q, cache_trees, cache_forests, seed
          )
          res.append(_to_nx(g, nodes, roots=set(rs)))
      return res
  
imports: import warnings
  from collections import Counter, defaultdict
  from math import comb, factorial
  import networkx
  from networkx.utils import py_random_state
label_desc: Use image node_id 15 for calling a global function with example usage: random_unlabeled_rooted_forest(n) and returns: res, _to_nx