We characterize the performance measure of a multi-agent system that is controlled by a distributed feedback control law. The agents may acquire the relative feedback on an undirected graph. Furthermore, a subset of them are aware of their full state; i.e. connected to a (possibly virtual) leader. We show the performance measure is a spectral function of the loopy graph Laplacian; i.e. the sum of a so-called performance function over Laplacian eigenvalues. This generalizes the existing results for the performance metrics in the formation control of integrator agents. The linear algebraic evaluation of these functions is independent of the network size. It turns out that using random sampling methods, we may approximate the performance measure without eigendecompositions. This observation benefits us in the optimal reweighting problem of a network graph. Moreover, the optimal feedback gains may be synthesized efficiently. Indeed, we introduce a framework that allows one to effectively optimize the networks of general linear time-invariant subsystems. We illustrate the practical aspects of our theoretical contributions by applying the methodology to systems of various dynamics, including the platooning of vehicles and formations of integrator agents.