Title: Defective eigenvalues for the non-backtracking matrix
Abstract: The non-backtracking (NB) matrix of a graph is the transition matrix of a random walk on the graph which cannot traverse the same edge in succession. This NB matrix and its properties of its eigenvalues have garnered interest of late, particularly in application to network analysis. However, the lack of symmetry in the NB matrix allows for the existence of graphs without a full basis of NB eigenvectors thus making the eigenvalue defective. In this talk, we will consider the fairly rare existence of such graphs and investigate defective eigenvalues for some infinite families.
This is joint work with Kristin Heysse and Carolyn Reinhart. This work is supported by the Simons Laufer Mathematical Sciences Institute and American Institute of Mathematics and the National Science Foundation.