  It is well-known that the eigenvalue spectrum of the Laplacian matrix of a
network contains valuable information about the network structure and the
behavior of many dynamical processes run on it. In this paper, we propose a
fully decentralized algorithm that iteratively modifies the structure of a
network of agents in order to control the moments of the Laplacian eigenvalue
spectrum. Although the individual agents have knowledge of their local network
structure only (i.e., myopic information), they are collectively able to
aggregate this local information and decide on what links are most beneficial
to be added or removed at each time step. Our approach relies on gossip
algorithms to distributively compute the spectral moments of the Laplacian
matrix, as well as ensure network connectivity in the presence of link
deletions. We illustrate our approach in nontrivial computer simulations and
show that a good final approximation of the spectral moments of the target
Laplacian matrix is achieved for many cases of interest.
