Consistency of spectral clustering in stochastic block models

  title={Consistency of spectral clustering in stochastic block models},
  author={Jing Lei and Alessandro Rinaldo},
  journal={Annals of Statistics},
We analyze the performance of spectral clustering for community extraction in stochastic block models. We show 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. This result applies to some popular polynomial time spectral clustering algorithms and is further extended to degree corrected stochastic… 

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