# Regularized Stochastic Block Model for robust community detection in complex networks

## TL;DR

This paper introduces a regularized stochastic block model that stabilizes community detection in complex networks by controlling internal degree ratios, enabling reliable inference of assortative or disassortative structures.

## Contribution

A novel regularized model that guides inference algorithms to accurately detect different community structures, overcoming local optima issues in traditional models.

## Key findings

- The regularized model converges quickly to the desired community structure.
- It reliably detects assortative or disassortative patterns based on a single parameter.
- It outperforms degree-corrected stochastic block models in complex networks.

## Abstract

The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing pattern is desired, the inference algorithms, which discover the most likely partition of the networks nodes, are likely to get trapped in the local optima of the log-likelihood. Here we introduce a new model constraining nodes' internal degrees ratios in the objective function to stabilize the inference of block models from the observed network data. Given the regularized model, the inference algorithms, such as Markov chain Monte Carlo, reliably finds assortative or disassortive structure as directed by the value of a single parameter. We show experimentally that the inference of our proposed model quickly converges to the desired assortative or disassortative partition while the inference of degree-corrected stochastic block model gets often trapped at the inferior local optimal partitions when the traditional assortative community structure is not strong in the observed networks.