Geometric and spectral theory of signed graphs

A signed graph is a graph whose edges are labelled by a signature. It serves as a simple model of discrete vector bundle. The fundamental ideas of balance and switching of signed graphs often lead to more systematic understanding of various parts of graph theory. In this talk, I will explain two such cases: a unification of Cheeger inequality and Bauer-Jost dual Cheeger inequality, and a unification of the discrete nodal domain theorem due to Davis, Galdwell, Leydold and Stadler, and Fiedler's approach on eigenvectors of acyclic matrices.

This talk is based on joint works with Fatihcan Atay, Chuanyuan Ge.