A central limit theorem for the giant in a stochastic block model

TL;DR

This paper proves a central limit theorem for the size of the giant component in a super-critical stochastic block model, simplifying previous proofs and connecting to classical Erdős-Rényi results.

Contribution

It introduces a simplified proof of the CLT for the giant component in stochastic block models, extending classical results to a more complex network setting.

Findings

Establishes a CLT for the giant component in stochastic block models.

Reduces the proof to the classic Erdős-Rényi case.

Provides a new perspective using breadth-first walk techniques.

Abstract

We provide a simple proof for of the central limit theorem for the number of vertices in the giant for super-critical stochastic block model using the breadth-first walk of Konarovskyi, Limic and the author (2024). Our approach follows the recent work of Corujo, Limic and Lemaire (2024) and reduces to the classic central limit theorem for the Erd\H{o}s-R\'{e}nyi model obtained by Stepanov (1970).