# Braess's paradox for the spectral gap in random graphs and delocalization of eigenvectors

@article{Eldan2017BraesssPF, title={Braess's paradox for the spectral gap in random graphs and delocalization of eigenvectors}, author={Ronen Eldan and Mikl{\'o}s Z. R{\'a}cz and T. Schramm}, journal={Random Struct. Algorithms}, year={2017}, volume={50}, pages={584-611} }

We study how the spectral gap of the normalized Laplacian of a random graph changes when an edge is added to or removed from the graph. There are known examples of graphs where, perhaps counter-intuitively, adding an edge can decrease the spectral gap, a phenomenon that is analogous to Braess's paradox in traffic networks. We show that this is often the case in random graphs in a strong sense. More precisely, we show that for typical instances of Erdi¾?s-Renyi random graphs Gn, p with constant… CONTINUE READING

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