A measure of dissimilarity between diffusive processes on networks

In this paper, we present a framework to compare the differences in occupation probabilities of two random walk processes, which can be generated by modifications network or transition between nodes same network. We explore dissimilarity measure defined terms eigenvalues and eigenvectors normalized Laplacian each process. This formalism is implemented examine diffusive dynamics described circulant matrices, effect new edges, rewiring networks as well evaluate divergences transport degree-biased walks with stochastic reset. Our results provide general tool dynamical processes on considering evolution states capturing complexity these structures.