  The Artificial Benchmark for Community Detection (ABCD) graph is a random
graph model with community structure and power-law distribution for both
degrees and community sizes. The model generates graphs with similar properties
as the well-known LFR one, and its main parameter $\xi$ can be tuned to mimic
its counterpart in the LFR model, the mixing parameter $\mu$.
  In this paper, we investigate various theoretical asymptotic properties of
the ABCD model. In particular, we analyze the modularity function, arguably,
the most important graph property of networks in the context of community
detection. Indeed, the modularity function is often used to measure the
presence of community structure in networks. It is also used as a quality
function in many community detection algorithms, including the widely used
Louvain algorithm.
