  In this paper we present a decentralized algorithm to estimate the
eigenvalues of the Laplacian matrix that encodes the network topology of a
multi-agent system. We consider network topologies modeled by undirected
graphs. The basic idea is to provide a local interaction rule among agents so
that their state trajectory is a linear combination of sinusoids oscillating
only at frequencies function of the eigenvalues of the Laplacian matrix. In
this way, the problem of decentralized estimation of the eigenvalues is mapped
into a standard signal processing problem in which the unknowns are the finite
number of frequencies at which the signal oscillates.
