powerlaw_cluster_graph

powerlaw_cluster_graph(n, m, p, seed=None, *, create_using=None)

Holme and Kim algorithm for growing graphs with powerlaw degree distribution and approximate average clustering.

Parameters:

nint

the number of nodes

mint

the number of random edges to add for each new node

pfloat,

Probability of adding a triangle after adding a random edge

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

create_usingGraph constructor, optional (default=nx.Graph)

Graph type to create. If graph instance, then cleared before populated. Multigraph and directed types are not supported and raise a NetworkXError.

Raises:

NetworkXError

If m does not satisfy 1 <= m <= n or p does not satisfy 0 <= p <= 1.

Notes

The average clustering has a hard time getting above a certain cutoff that depends on m. This cutoff is often quite low. The transitivity (fraction of triangles to possible triangles) seems to decrease with network size.

It is essentially the Barabási–Albert (BA) growth model with an extra step that each random edge is followed by a chance of making an edge to one of its neighbors too (and thus a triangle).

This algorithm improves on BA in the sense that it enables a higher average clustering to be attained if desired.

It seems possible to have a disconnected graph with this algorithm since the initial m nodes may not be all linked to a new node on the first iteration like the BA model.

References

[1]

P. Holme and B. J. Kim, “Growing scale-free networks with tunable clustering”, Phys. Rev. E, 65, 026107, 2002.