Self-Organization of Weighted Networks for Optimal Synchronizability

We show that a network can self-organize its existing topology, i.e., by adapting edge weights, in a completely decentralized manner in order to maximize its synchronizability while satisfying local constraints: we look specifically at nonnegativity of edge weights and maximum weighted degree of nodes. A novel multilayer approach is presented, which uses a decentralized strategy through which each node can estimate one of two spectral functions of the graph Laplacian, the algebraic connectivity lambda(2), or 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 globally optimal values for the edge weights for the synchronization of a network of coupled systems.