# Adapting Stochastic Block Models to Power-Law Degree Distributions

## TL;DR

This paper introduces PLD-SBM, a novel stochastic block model variant that explicitly models power-law degree distributions in networks, improving community detection accuracy in real-world data.

## Contribution

The paper proposes PLD-SBM, incorporating degree decay variables with an exponential prior to better capture scale-free network features and correct biases in traditional SBMs.

## Key findings

- PLD-SBM effectively models power-law degree distributions.
- It improves cluster prediction accuracy on real-world networks.
- The model preserves scale-free properties in synthetic and real data.

## Abstract

Stochastic block models (SBMs) have been playing an important role in modeling clusters or community structures of network data. But, it is incapable of handling several complex features ubiquitously exhibited in real-world networks, one of which is the power-law degree characteristic. To this end, we propose a new variant of SBM, termed power-law degree SBM (PLD-SBM), by introducing degree decay variables to explicitly encode the varying degree distribution over all nodes. With an exponential prior, it is proved that PLD-SBM approximately preserves the scale-free feature in real networks. In addition, from the inference of variational E-Step, PLD-SBM is indeed to correct the bias inherited in SBM with the introduced degree decay factors. Furthermore, experiments conducted on both synthetic networks and two real-world datasets including Adolescent Health Data and the political blogs network verify the effectiveness of the proposed model in terms of cluster prediction accuracies.