Spectral theory for dynamics on undirected and directed graphs containing only attractive (or positive) interactions has been the subject of detailed research studies. However, in many applied problems, these graphs can carry interactions which are repulsive (or negative) to a certain degree. Here, we report results of the influence of signs on the spectral properties of and dynamics on expander graphs and highlight its importance. To this end, we consider Lubotzky-Phillips-Sarnak Ramanujan graphs and their edge-rewired analogs.
*Work jointly done with Dr. Michael S. Cavers at the University of Toronto Mississauga