Spectral clustering has become one of the most popular algorithms in data clustering and
community detection. We study the performance of classical two-step spectral clustering via
the graph Laplacian to learn the stochastic block model. Our aim is to answer the following
question: when is spectral clustering via the graph Laplacian able to achieve strong
consistency, ie, the exact recovery of the underlying hidden communities? Our work
provides an entrywise analysis (an ℓ1-norm perturbation bound) of the Fiedler eigenvector …

Spectral clustering has become one of the most popular algorithms in data clustering and
community detection. We study the performance of classical two-step spectral clustering via
the graph Laplacian to learn the stochastic block model. Our aim is to answer the following
question: when is spectral clustering via the graph Laplacian able to achieve strong
consistency, ie, the exact recovery of the underlying hidden communities? Our work
provides an entrywise analysis (an $\ell_ {\infty} $-norm perturbation bound) of the Fielder …