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

Lennart Gulikers 1, 2, 3 Marc Lelarge 1, 3 Laurent Massoulié 2
3 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : We consider community detection in Degree-Corrected Stochastic Block Models. We perform spectral clustering on $\widehat{H} = \left(\frac{1}{\widehat{D}_i \widehat{D}_j} A_{ij} \right)_{i,j=1}^n,$ where $A$ is the adjacency matrix of the network containing $n$ vertices and $\widehat{D}_i$ is the observed degree of node $i$. We show that this leads to consistent recovery of the block-membership of all but a vanishing fraction of nodes, even when the lowest degree is of order log$(n)$. There turns out to be a natural connection between $\widehat{H}$ and random walks on instances of the random graph. Moreover, $\widehat{H}$ appears to have a better behaved eigenspace than the ordinary adjacency matrix in case of a very heterogeneous degree-sequence.
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https://hal.archives-ouvertes.fr/hal-01258191
Contributor : Marc Lelarge <>
Submitted on : Monday, January 18, 2016 - 5:24:38 PM
Last modification on : Thursday, October 17, 2019 - 12:36:05 PM

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  • HAL Id : hal-01258191, version 1
  • ARXIV : 1506.08621

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Lennart Gulikers, Marc Lelarge, Laurent Massoulié. A spectral method for community detection in moderately-sparse degree-corrected stochastic block models. 2016. ⟨hal-01258191⟩

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