This documents the development version of NetworkX. Documentation for the current release can be found here.


random_k_out_graph(n, k, alpha, self_loops=True, seed=None)[source]

Returns a random k-out graph with preferential attachment.

A random k-out graph with preferential attachment is a multidigraph generated by the following algorithm.

  1. Begin with an empty digraph, and initially set each node to have weight alpha.

  2. Choose a node u with out-degree less than k uniformly at random.

  3. Choose a node v from with probability proportional to its weight.

  4. Add a directed edge from u to v, and increase the weight of v by one.

  5. If each node has out-degree k, halt, otherwise repeat from step 2.

For more information on this model of random graph, see [1].


The number of nodes in the returned graph.


The out-degree of each node in the returned graph.


A positive float representing the initial weight of each vertex. A higher number means that in step 3 above, nodes will be chosen more like a true uniformly random sample, and a lower number means that nodes are more likely to be chosen as their in-degree increases. If this parameter is not positive, a ValueError is raised.


If True, self-loops are allowed when generating the graph.

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.


A k-out-regular multidigraph generated according to the above algorithm.


If alpha is not positive.


The returned multidigraph may not be strongly connected, or even weakly connected.


[1]: Peterson, Nicholas R., and Boris Pittel.

“Distance between two random k-out digraphs, with and without preferential attachment.” arXiv preprint arXiv:1311.5961 (2013). <>