We initialize the solution matrix same as the input graph matrix as a first step. Then we update the solution matrix by considering all vertices as an intermediate vertex. The idea is to one by one ...

a 1 ≤ μ ≤ μ 2. μ = μ 2 = 1 if the reversal of the graph is a directed tree. If the Laplacian matrix L is a normal matrix, then a 1 = μ = μ 2 and G is connected ⇔ G is strongly connected. C. W. Wu, ...

Abstract: 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 ...

We establish that, as long as the (generally directed) graph that describes the communication links between components is strongly connected, each of the proposed matrix scaling algorithms allows the ...