Concentration and regularization of random graphs

@article{Le2017ConcentrationAR,
  title={Concentration and regularization of random graphs},
  author={Can M. Le and Elizaveta Levina and Roman Vershynin},
  journal={ArXiv},
  year={2017},
  volume={abs/1506.00669}
}
  • Can M. Le, Elizaveta Levina, Roman Vershynin
  • Published in Random Struct. Algorithms 2017
  • Computer Science, Mathematics
  • This paper studies how close random graphs are typically to their expectations. We interpret this question through the concentration of the adjacency and Laplacian matrices in the spectral norm. We study inhomogeneous Erd\"os-R\'enyi random graphs on $n$ vertices, where edges form independently and possibly with different probabilities $p_{ij}$. Sparse random graphs whose expected degrees are $o(\log n)$ fail to concentrate; the obstruction is caused by vertices with abnormally high and low… CONTINUE READING

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