Properties and Performance of the ABCDe Random Graph Model with Community Structure

Despite the fact that this is clearly a very good model, it is known to have some scalability limitations and it is challenging to analyze it theoretically. Moreover, the mixing parameter µ, the main parameter of the model guiding the strength of the communities, has a non-obvious interpretation and so can lead to unnaturally-defined networks, see [2] for a detailed discussion. An alternative random graph model with community structure and power-law distribution for both degrees and community sizes is the Artificial Benchmark for Community Detection graph (ABCD). In [2] it is shown that the new model is fast, simple, and can be easily tuned to allow the user to make a smooth transition between the two extremes: pure (disjoint) communities and random graph with no community structure. Moreover, in [3] the modularity function of ABCD is theoretically analyzed and it is confirmed that its asymptotic behaviour is consistent with simulations on smaller experimental graphs.