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}
}
  • Ronen Eldan, Miklós Z. Rácz, T. Schramm
  • Published 2017
  • Mathematics, Computer Science
  • Random Struct. Algorithms
  • 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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