Null-adjusted persistence function for high-resolution community detection

Modularity and persistence probability are two widely used quality functions for detecting communities in complex networks. In this paper, we introduce a new objective function called null-adjusted persistence, which incorporates features from both modularity and persistence probability, as it implies a comparison of persistence probability with the same configuration null model of modularity. We prove key analytic properties of this new function, demonstrating that it successfully addresses modularity’s well-known scaling and resolution limitations, as well as the monotonic bias of persistence probability with respect to cluster size. To optimize this new function, we adapt the Louvain method and evaluate our approach on both synthetic benchmarks and real-world networks. Our results show that maximizing null-adjusted persistence consistently yields higher-resolution partitions than standard modularity maximization, particularly in large real networks.