On properties of a particular class of directed graphs used in stability analysis of flocking algorithms

In this paper, we present sufficient conditions to address a larger class of digraphs, including balanced ones, whose members´ Laplacian (L) makes L₁L + L^TL₁ to be positive semi-definite, where L₁ is the Laplacian associated with a fully connected equally-edged weighted graphs. This property can be later utilized to introduce an appropriate energy function for stability analysis of flocking algorithms in a larger class of networks with switching directed information flow. Also, some of their properties are investigated in the line of matrix theory and graph theory.