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 λ
₂
, or 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 minimizer, and, hence, achieve globally optimal values for the edge weights for the synchronization of a network of coupled systems.