# Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges

@article{Oliveira2010ConcentrationOT, title={Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges}, author={Roberto Imbuzeiro Oliveira}, journal={arXiv: Combinatorics}, year={2010} }

Consider any random graph model where potential edges appear independently, with possibly different probabilities, and assume that the minimum expected degree is !(lnn). We prove that the adjacency matrix and the Laplacian of that random graph are concentrated around the corresponding matrices of the weighted graph whose edge weights are the probabilities in the random model. We apply this result to two different settings. In bond percolation, we show that, whenever the minimum expected degree…

## 174 Citations

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