networkx.generators.directed.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 thank
uniformly at random. - Choose a node
v
from with probability proportional to its weight. - Add a directed edge from
u
tov
, and increase the weight ofv
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: - 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
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, aValueError
is raised. - self_loops (bool) – If True, self-loops are allowed when generating the graph.
- seed (int) – If provided, this is used as the seed for the random number generator.
Returns: A
k
-out-regular multidigraph generated according to the above algorithm.Return type: MultiDiGraph
Raises: ValueError
– Ifalpha
is not positive.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>
- Begin with an empty digraph, and initially set each node to have
weight