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A spectral method for community detection in moderately sparse degree-corrected stochastic block models

Part of: Probability theory on algebraic and topological structures Graph theory Social and behavioral sciences: general topics Mathematical sociology Algorithms - Computer Science

Published online by Cambridge University Press:  08 September 2017

Lennart Gulikers ,
Marc Lelarge  and
Laurent Massoulié
Lennart Gulikers*
Affiliation:
Microsoft Research - INRIA Joint Centre and École Normale Supérieure
Marc Lelarge*
Affiliation:
INRIA and École Normale Supérieure
Laurent Massoulié*
Affiliation:
Microsoft Research - INRIA Joint Centre
*
* Postal address: Microsoft Research - Inria Joint Centre, Campus de l'École Polytechnique, Bâtiment Alan Turing, 1 rue Honoré d'Estienne d'Orves, 91120 Palaiseau, France.
*** Postal address: Inria Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France. Email address: marc.lelarge@ens.fr
* Postal address: Microsoft Research - Inria Joint Centre, Campus de l'École Polytechnique, Bâtiment Alan Turing, 1 rue Honoré d'Estienne d'Orves, 91120 Palaiseau, France.
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Abstract

We consider community detection in degree-corrected stochastic block models. We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the block membership of all but a vanishing fraction of nodes, in the regime where the lowest degree is of order log(n) or higher. Recovery succeeds even for very heterogeneous degree distributions. The algorithm does not rely on parameters as input. In particular, it does not need to know the number of communities.

Keywords

Social and information networkrandom graphdegree-corrected stochastic block modelspectral algorithmmachine learning05C80

MSC classification

Primary: 91D30: Social networks
Secondary: 05C80: Random graphs 60B20: Random matrices (probabilistic aspects; for algebraic aspects see ) 68W40: Analysis of algorithms 91C20: Clustering
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 3 , September 2017 , pp. 686 - 721
Copyright
Copyright © Applied Probability Trust 2017 

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