Self-organization of weighted networks for optimal synchronizability
This work addresses the problem of distributed network optimization for synchronization, which is relevant for multi-agent systems and complex networks.
The paper presents a distributed, self-organizing method for weighted networks to optimize synchronizability by maximizing algebraic connectivity or minimizing the eigenratio, achieving optimal structure under local constraints.
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 $λ_2$ and the eigenratio $r = λ_n / λ_2$ . These local estimates are then used to evolve the edge weights so as to maximize $λ_2$, or minimize $r$ and, hence, achieve an optimal structure.