# Spectral clustering and the high-dimensional stochastic blockmodel

@article{Rohe2011SpectralCA, title={Spectral clustering and the high-dimensional stochastic blockmodel}, author={Karl Rohe and Sourav Chatterjee and Bin Yu}, journal={Annals of Statistics}, year={2011}, volume={39}, pages={1878-1915} }

Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social ne tworks, representing people who communicate with each other, are one example. Communities or clusters of highly connected actors form an essential feature in the structure of several empirical networks. Spectral clustering is a popular and computationally feasi ble method to discover these communities. The Stochastic Block Model (Holland et al., 1983) is a…

## 797 Citations

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It is shown that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\log n$ with $n$ the number of nodes.

### Latent structure blockmodels for Bayesian spectral graph clustering

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A class of models called latent structure block models (LSBM) is proposed, allowing for graph clustering when community-specific one-dimensional manifold structure is present, and is shown to have a good performance on simulated and real-world network data.

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It is shown that the algorithm can recover the hidden communities with vanishing misclustering rate even when the expected node degrees grow only logarithmically in the size of the network.

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