# networkx.generators.duplication.partial_duplication_graph¶

partial_duplication_graph(N, n, p, q, seed=None)[source]

Returns a random graph using the partial duplication model.

Parameters
• 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.

Notes

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 N nodes have been reached.

1. A random node, u, is picked and a new node, v, is created.

2. For each neighbor of u an edge from the neighbor to v is created with probability p.

3. An edge from u to v is created with probability q.

This algorithm appears in [1].

This implementation allows the possibility of generating disconnected graphs.

References

1

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>