One of my papers was just published in final form. Here are some details.
Title: Dynamical Importance and Network Perturbations
Authors: Ethan Young and Mason A. Porter
Abstract: The leading eigenvalue λ of the adjacency matrix of a graph exerts much influence on the behavior of
dynamical processes on that graph. It is thus relevant to relate notions of importance of network structures to λ
and its associated eigenvectors. We study a previously derived measure of edge importance known as “dynamical
importance,” which estimates how much λ changes when one removes an edge from a graph or adds an edge
to it. We examine the accuracy of this estimate for several undirected network structures and compare it to
the relative change in λ after an edge removal or edge addition. We then derive a first-order approximation of
the change in the leading eigenvector. We also consider the effects of edge additions on Kuramoto dynamics on
networks, and we express the Kuramoto order parameter in terms of dynamical importance. Through our analysis
and computational experiments, we find that studying dynamical importance can improve understanding of the
relationship between network perturbations and dynamical processes on networks.
3 days ago
