random_unlabeled_rooted_tree(n, *, number_of_trees=None, seed=None)[source]#

Returns a number of unlabeled rooted trees uniformly at random

Returns one or more (depending on number_of_trees) unlabeled rooted trees with n nodes drawn uniformly at random.


The number of nodes

number_of_treesint or None (default)

If not None, this number of trees is generated and returned.

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

networkx.Graph or list of networkx.Graph

A single networkx.Graph (or a list thereof, if number_of_trees is specified) with nodes in the set {0, …, n - 1}. The “root” graph attribute identifies the root of the tree.


If n is zero (because the null graph is not a tree).


The trees are generated using the “RANRUT” algorithm from [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_trees optional argument to reuse the counting functions.



Nijenhuis, Albert, and Wilf, Herbert S. “Combinatorial algorithms: for computers and calculators.” Academic Press, 1978. https://doi.org/10.1016/C2013-0-11243-3