An isoperimetric constant for signed graphs

Abstract

A sign is introduced in the usual Laplacian on graphs and the corresponding analogue of the isoperimetric constant for this Laplacian is presented, i.e. a geometric quantity which enables to bound from above and below the first eigenvalue. The introduction of the sign in the Laplacian is motivated by the study of $2$-lifts of graphs and of the combinatorial Laplacian in higher degree.

10 pages

References in corpus (1)

• Cheeger constants, structural balance, and spectral clustering analysis for signed graphs

Cited by in corpus (2)

• De-Signing Hamiltonians for Quantum Adiabatic Optimization
• Quantum ground state isoperimetric inequalities for the energy spectrum of local Hamiltonians