  We propose a method to efficiently estimate the Laplacian eigenvalues of an
arbitrary, unknown network of interacting dynamical agents. The inputs to our
estimation algorithm are measurements about the evolution of a collection of
agents (potentially one) during a finite time horizon; notably, we do not
require knowledge of which agents are contributing to our measurements. We
propose a scalable algorithm to exactly recover a subset of the Laplacian
eigenvalues from these measurements. These eigenvalues correspond directly to
those Laplacian modes that are observable from our measurements. We show how
our technique can be applied to networks of multiagent systems with arbitrary
dynamics in both continuous- and discrete-time. Finally, we illustrate our
results with numerical simulations.

Spectral Theory;Optimization and Control