random_k_out_graph#

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.

Begin with an empty digraph, and initially set each node to have weight alpha.
Choose a node u with out-degree less than k uniformly at random.
Choose a node v from with probability proportional to its weight.
Add a directed edge from u to v, and increase the weight of v by one.
If each node has out-degree k, halt, otherwise repeat from step 2.

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

Parameters:

nint: The number of nodes in the returned graph.
kint: The out-degree of each node in the returned graph.
alphafloat: 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.
self_loopsbool: If True, self-loops are allowed when generating the graph.
seedinteger, random_state, or None (default): Indicator of random number generation state. See Randomness.

Returns:

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

Raises:

Notes

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

References

[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). <https://arxiv.org/abs/1311.5961>