Self-organization of weighted networks for optimal synchronizability

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.

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