Simplify to Amplify: Achieving Information-Theoretic Bounds with Fewer Steps in Spectral Community Detection

TL;DR

This paper introduces a simplified spectral algorithm for community detection in stochastic block models that achieves near-optimal error bounds with fewer steps, improving both efficiency and accuracy.

Contribution

The authors develop a streamlined spectral method that directly utilizes adjacency matrix properties to reach information-theoretic bounds, reducing complexity compared to prior approaches.

Findings

Achieves error bounds close to theoretical limits

Reduces algorithmic complexity by removing preprocessing steps

Demonstrates practical effectiveness through experiments

Abstract

We propose a streamlined spectral algorithm for community detection in the two-community stochastic block model (SBM) under constant edge density assumptions. By reducing algorithmic complexity through the elimination of non-essential preprocessing steps, our method directly leverages the spectral properties of the adjacency matrix. We demonstrate that our algorithm exploits specific characteristics of the second eigenvalue to achieve improved error bounds that approach information-theoretic limits, representing a significant improvement over existing methods. Theoretical analysis establishes that our error rates are tighter than previously reported bounds in the literature. Comprehensive experimental validation confirms our theoretical findings and demonstrates the practical effectiveness of the simplified approach. Our results suggest that algorithmic simplification, rather than increasing complexity, can lead to both computational efficiency and enhanced performance in spectral community detection.