# EXIT Analysis for Community Detection

## TL;DR

This paper applies the EXIT method to analyze belief propagation in community detection, providing insights into phase transitions and the impact of side information on detection performance.

## Contribution

It introduces EXIT analysis to community detection, enabling prediction of phase transitions and understanding the role of side information in belief propagation.

## Key findings

- EXIT predicts asymptotic phase transition for weak recovery
- EXIT analysis reveals the effect of side information on residual errors
- Generalizes previous results to finite-alphabet side information

## Abstract

This paper employs the extrinsic information transfer (EXIT) method, a technique imported from the analysis of the iterative decoding of error control codes, to study the performance of belief propagation in community detection in the presence of side information. We consider both the detection of a single (hidden) community, as well as the problem of identifying two symmetric communities. For single community detection, this paper demonstrates the suitability of EXIT to predict the asymptotic phase transition for weak recovery. More importantly, EXIT analysis is leveraged to produce useful insights such as the performance of belief propagation near the threshold. For two symmetric communities, the asymptotic residual error for belief propagation is calculated under finite-alphabet side information, generalizing a previous result with noisy labels. EXIT analysis is used to illuminate the effect of side information on community detection, its relative importance depending on the correlation of the graphical information with node labels, as well as the effect of side information on residual errors.