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