# networkx.generators.directed.scale_free_graph¶

scale_free_graph(n, alpha=0.41, beta=0.54, gamma=0.05, delta_in=0.2, delta_out=0, create_using=None, seed=None)[source]

Returns a scale-free directed graph.

Parameters: n (integer) – Number of nodes in graph alpha (float) – Probability for adding a new node connected to an existing node chosen randomly according to the in-degree distribution. beta (float) – Probability for adding an edge between two existing nodes. One existing node is chosen randomly according the in-degree distribution and the other chosen randomly according to the out-degree distribution. gamma (float) – Probability for adding a new node connected to an existing node chosen randomly according to the out-degree distribution. delta_in (float) – Bias for choosing ndoes from in-degree distribution. delta_out (float) – Bias for choosing ndoes from out-degree distribution. create_using (NetworkX graph constructor, optional) – The default is a MultiDiGraph 3-cycle. If a graph instance, use it without clearing first. If a graph constructor, call it to construct an empty graph. seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.

Examples

Create a scale-free graph on one hundred nodes:

>>> G = nx.scale_free_graph(100)


Notes

The sum of alpha, beta, and gamma must be 1.

References

 [1] B. Bollobás, C. Borgs, J. Chayes, and O. Riordan, Directed scale-free graphs, Proceedings of the fourteenth annual ACM-SIAM Symposium on Discrete Algorithms, 132–139, 2003.