Isospectral Graph Reductions

Abstract

Let G be an arbitrary finite weighted digraph with weights in the set of complex rational functions. A general procedure is proposed which allows for the reduction of G to a smaller graph with a less complicated structure having the same spectrum as of G (up to some set known in advance). The proposed procedure has a lot of flexibility and could be used e.g. for design of networks with prescribed spectral and dynamical properties.

21 pages with 8 figures. Revised version has a main result (theorem 7.2) more clearly stated