partial_duplication_graph(N, n, p, q, seed=None)¶
Returns a random graph using the partial duplication model.
N (int) – The total number of nodes in the final graph.
n (int) – The number of nodes in the initial clique.
p (float) – The probability of joining each neighbor of a node to the duplicate node. Must be a number in the between zero and one, inclusive.
q (float) – The probability of joining the source node to the duplicate node. Must be a number in the between zero and one, inclusive.
seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.
A graph of nodes is grown by creating a fully connected graph of size
n. The following procedure is then repeated until a total of
Nnodes have been reached.
A random node, u, is picked and a new node, v, is created.
For each neighbor of u an edge from the neighbor to v is created with probability
An edge from u to v is created with probability
This algorithm appears in .
This implementation allows the possibility of generating disconnected graphs.
Knudsen Michael, and Carsten Wiuf. “A Markov chain approach to randomly grown graphs.” Journal of Applied Mathematics 2008. <https://doi.org/10.1155/2008/190836>