Rate-Distortion Function of the Stochastic Block Model

TL;DR

This paper characterizes the lossy compression limits of stochastic block model graphs using information theory, deriving the rate-distortion function with community labels as side information, and extends results to Erdős-Rényi graphs.

Contribution

It provides the first derivation of the rate-distortion function for SBM graphs with community information as side data, advancing understanding of lossy network compression.

Findings

Derived the conditional rate-distortion function for SBM with community labels.

Extended the analysis to Erdős-Rényi random graphs.

Formulated the problem as a Wyner-Ziv lossy compression scenario.

Abstract

The stochastic block model (SBM) is extensively used to model networks in which users belong to certain communities. In recent years, the study of information-theoretic compression of such networks has gained attention, with works primarily focusing on lossless compression. In this work, we address the lossy compression of SBM graphs by characterizing the rate-distortion function under a Hamming distortion constraint. Specifically, we derive the conditional rate-distortion function of the SBM with community membership as side information. We approach this problem as the classical Wyner-Ziv lossy problem by minimising mutual information of the graph and its reconstruction conditioned on community labels. Lastly, we also derive the rate-distortion function of the Erd\H{o}s-R\'enyi (ER) random graph model.