random_k_out_graph(n, k, alpha, self_loops=True, seed=None)¶
Returns a random
k-out graph with preferential attachment.
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
Choose a node
uwith out-degree less than
kuniformly at random.
Choose a node
vfrom with probability proportional to its weight.
Add a directed edge from
v, and increase the weight of
If each node has out-degree
k, halt, otherwise repeat from step 2.
For more information on this model of random graph, see .
n (int) – The number of nodes in the returned graph.
k (int) – The out-degree of each node in the returned graph.
alpha (float) – A positive
floatrepresenting 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
self_loops (bool) – If True, self-loops are allowed when generating the graph.
seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.
k-out-regular multidigraph generated according to the above algorithm.
- Return type
ValueError – If
alphais not positive.
The returned multidigraph may not be strongly connected, or even weakly connected.
- : 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>