Publication Type

Working Paper

Version

submittedVersion

Publication Date

8-2019

Abstract

In this paper we prove the strong consistency of several methods based on the spectral clustering techniques that are widely used to study the community detection problem in stochastic block models (SBMs). We show that under some weak conditions on the minimal degree, the number of communities, and the eigenvalues of the probability block matrix, the K-means algorithm applied to the eigenvectors of the graph Laplacian associated with its first few largest eigenvalues can classify all individuals into the true community uniformly correctly almost surely. Extensions to both regularized spectral clustering and degree-corrected SBMs are also considered. We illustrate the performance of different methods on simulated networks.

Keywords

Community detection, degree-corrected stochastic block model, K-means, regularization, strong consistency.

Discipline

Econometrics

Research Areas

Econometrics

First Page

1

Last Page

64

Copyright Owner and License

Authors

Additional URL

https://arxiv.org/abs/1710.06191

Included in

Econometrics Commons

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