Eigenvalue Assignment for the Laplacian Matrix of Directed Graphs
Jonathan Hermann, Ulrich Konigorski · 2019
This paper considers the problem of designing the edge weights of directed graphs such that their Laplacian matrix has a prescribed spectrum. We provide a parametrization of the Laplacian matrix which is suitable for solving the problem numerically. We show how the edge weights can be further optimized to achieve secondary design goals and give an application example by designing the communication topology of a multi-agent system. Besides the general case of graphs with arbitrarily many vertices, we consider some special cases for small graphs and provide deeper insight into the solution to the problem in these cases.