Self-organization of weighted networks for optimal synchronizability

Abstract

We show that a network can self-organize its structure in a completely distributed manner in order to optimize its synchronizability whilst satisfying the local constraints: non-negativity of edge weights, and maximum weighted degree of nodes. A novel multilayer approach is presented which uses a distributed strategy to estimate two spectral functions of the graph Laplacian, the algebraic connectivity ${\lambda }_2$ and the eigenratio $r={\lambda }_n/{\lambda }_2$ . These local estimates are then used to evolve the edge weights so as to maximize ${\lambda }_2$, or minimize $r$ and, hence, achieve an optimal structure.