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-seq...
Networks or graphs can easily represent a diverse set of data sources that are characterized by inte...
PDF includes supplement with proofs, lemmas and additional simulation results.</p
PDF includes supplement with proofs, lemmas and additional simulation results.</p
International audience—This article proposes a new spectral method for community detection in large ...
International audience—This article proposes a new spectral method for community detection in large ...
International audienceSpectral algorithms are classic approaches to clustering and community detecti...
International audienceSpectral algorithms are classic approaches to clustering and community detecti...
International audienceSpectral algorithms are classic approaches to clustering and community detecti...
International audienceMotivated by community detection, we characterise the spectrum of the non-back...
International audienceThis article proposes a spectral analysis of dense random graphs generated by ...
International audienceThis article proposes a spectral analysis of dense random graphs generated by ...
International audienceThis article proposes a spectral analysis of dense random graphs generated by ...
PDF includes supplement with proofs, lemmas and additional simulation results.</p
Spectral clustering is a popular method for community detection in networks under the assumption of ...
PDF includes supplement with proofs, lemmas and additional simulation results.</p
Networks or graphs can easily represent a diverse set of data sources that are characterized by inte...
PDF includes supplement with proofs, lemmas and additional simulation results.</p
PDF includes supplement with proofs, lemmas and additional simulation results.</p
International audience—This article proposes a new spectral method for community detection in large ...
International audience—This article proposes a new spectral method for community detection in large ...
International audienceSpectral algorithms are classic approaches to clustering and community detecti...
International audienceSpectral algorithms are classic approaches to clustering and community detecti...
International audienceSpectral algorithms are classic approaches to clustering and community detecti...
International audienceMotivated by community detection, we characterise the spectrum of the non-back...
International audienceThis article proposes a spectral analysis of dense random graphs generated by ...
International audienceThis article proposes a spectral analysis of dense random graphs generated by ...
International audienceThis article proposes a spectral analysis of dense random graphs generated by ...
PDF includes supplement with proofs, lemmas and additional simulation results.</p
Spectral clustering is a popular method for community detection in networks under the assumption of ...
PDF includes supplement with proofs, lemmas and additional simulation results.</p
Networks or graphs can easily represent a diverse set of data sources that are characterized by inte...
PDF includes supplement with proofs, lemmas and additional simulation results.</p
PDF includes supplement with proofs, lemmas and additional simulation results.</p