Modularity of the ABCD Random Graph Model with Community Structure
This work provides foundational insights for researchers in network science and community detection, though it is incremental as it builds on existing models like LFR.
The paper investigates the theoretical asymptotic properties of the modularity function in the ABCD random graph model, which mimics the LFR model with community structure and power-law distributions, analyzing its behavior as a key measure for community detection.
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 $ξ$ can be tuned to mimic its counterpart in the LFR model, the mixing parameter $μ$. 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.