Abstract:
The purpose of this paper is to investigate methods for analyzing
networks from an algebraic perspective. The main focus will be
on the dominant eigenpair of the adjacency matrix representing a
graph, as many different centrality measures for networks are cast in
terms of eigenvalue problems. We will see how it is affected by small
perturbations to the graph and also propose methods for estimating
these changes. This analysis will be justified from the ground up,
only assuming basic elements of linear algebra.
