15.10.2018 16:15 Katie Fitch (TUM):
A new method for directed graph symmetrizationMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

In this talk I will present a new method for symmetrization of directed graphs that arises from the studying the steady state dynamics of a network under a simple noisy consensus process. The symmetrization method constructs an undirected graph with equivalent pairwise effective resistances as a given directed graph. Consequently a graph metric, square root of effective resistance, is preserved between the directed graph and its symmetrized version. I will show that the preservation of this metric allows for interpretation of algebraic and spectral properties of the symmetrized graph in the context of the directed graph, due to the relationship between effective resistance and the Laplacian spectrum. Additionally, I will demonstrate a decomposition procedure for directed graph Laplacian matrices and conclude with relevant applications.