Spectral Design of Dynamic Networks via Local Operations

摘要: Motivated by the relationship between eigenvalue spectrum of Laplacian matrix a network and behavior dynamical processes evolving in it, we propose distributed iterative algorithm which group $n$ autonomous agents self-organize structure their communication order to control network's spectrum. In our algorithm, assume that each agent has access only local (myopic) view around it. iteration, peform decentralized decision process determine edge addition/deletion minimizes distance function defined space spectra. This spectral presents interesting theoretical properties allow an efficient implementation process. Our is stable construction, i.e., locally optimizes spectrum, shown perform extremely well practice. We illustrate results with nontrivial simulations design networks matching complex networks, such as small-world power-law networks.