Article Source

• Spectra of Graphs and Hypergraphs

Spectra of Graphs and Hypergraphs

• Jürgen Jost (Max Planck institute for mathematics – Leipzig, Germany)
• Spectra of graphs and hypergraphs

Abstract

The spectral theory of the Laplace operator on graphs offers many analo-gies with that of Riemannian manifolds, like Cheeger type inequalities, but also shows some different phenomena. For hypergraphs, a main step consists in the definition of a Laplace operator that can also offer such analogies. Lovasz extensions of Rayleigh quotients can uncover some deeper reasons behind such analogies.