# 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.

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.

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:
ValueError

If `alpha` is not positive.

Notes

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

References

: 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>