random_tree#

random_tree(n, seed=None, create_using=None)[source]#

Returns a uniformly random tree on n nodes.

Parameters:

nint: A positive integer representing the number of nodes in the tree.
seedinteger, random_state, or None (default): Indicator of random number generation state. See Randomness.
create_usingNetworkX graph constructor, optional (default=nx.Graph): Graph type to create. If graph instance, then cleared before populated.

Returns:

NetworkX graph: A tree, given as an undirected graph, whose nodes are numbers in the set {0, …, n - 1}.

Raises:

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

Notes

The current implementation of this function generates a uniformly random Prüfer sequence then converts that to a tree via the from_prufer_sequence() function. Since there is a bijection between Prüfer sequences of length n - 2 and trees on n nodes, the tree is chosen uniformly at random from the set of all trees on n nodes.

Examples

>>> tree = nx.random_tree(n=10, seed=0)
>>> nx.write_network_text(tree, sources=[0])
╙── 0
    ├── 3
    └── 4
        ├── 6
        │   ├── 1
        │   ├── 2
        │   └── 7
        │       └── 8
        │           └── 5
        └── 9

>>> tree = nx.random_tree(n=10, seed=0, create_using=nx.DiGraph)
>>> nx.write_network_text(tree)
╙── 0
    ├─╼ 3
    └─╼ 4
        ├─╼ 6
        │   ├─╼ 1
        │   ├─╼ 2
        │   └─╼ 7
        │       └─╼ 8
        │           └─╼ 5
        └─╼ 9