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Central Limit Theorem for the Giant Component in the Stochastic Block Model

Above criticality the largest connected component of a stochastic block model occupies a positive fraction of the vertices. This concept covers the Gaussian fluctuation law for the class-by-class vertex counts of that giant component, proved by a breadth-first exploration walk that reduces the problem, through the delta method, to the classical Erdos-Renyi central limit theorem.

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A CENTRAL LIMIT THEOREM FOR THE GIANT IN A STOCHASTIC BLOCK MODEL DAVID CLANCY, JR. Abstract. We

In the sparse Erdos-Renyi random graph a giant connected component emerges above the critical threshold, and its relative size obeys a central limit theorem (Stepanov 1970). This paper extends that G…