Happy to share that our paper Nonlinear Spectral Graph Theory has been accepted for publication in the Survey and Review section of SIAM Review.

Joint work with Piero Deidda and Dong Zhang.

Nonlinear spectral graph theory extends classical spectral graph theory by connecting spectral properties of nonlinear operators on graphs with topological properties of the graph itself — connections that often become tighter when moving from the linear to the nonlinear setting. The paper gives a complete and self-contained introduction to the spectral theory of the graph p-Laplacian, surveying its links with higher-order Cheeger constants, sphere packing constants, independence and matching numbers, and proving new results that fill several gaps in the theory — in particular on the graph infinity Laplacian spectrum, its nodal domains, the variational spectrum of the p-Laplacian and its regularity in p, and new Cheeger constants related to the 1-Laplacian spectrum.