  The focus of this paper is to quantify measures of aggregate fluctuations for
a class of consensus-seeking multiagent networks subject to exogenous noise
with alpha-stable distributions. This type of noise is generated by a class of
random measures with heavy-tailed probability distributions. We define a
cumulative scale parameter using scale parameters of probability distributions
of the output variables, as a measure of aggregate fluctuation. Although this
class of measures can be characterized implicitly in closed-form in
steady-state, finding their explicit forms in terms of network parameters is,
in general, almost impossible. We obtain several tractable upper bounds in
terms of Laplacian spectrum and statistics of the input noise. Our results
suggest that relying on Gaussian-based optimal design algorithms will result in
non-optimal solutions for networks that are driven by non-Gaussian noise inputs
with alpha-stable distributions.
  The manuscript has been submitted for publication to IEEE Transactions on
Control of Network Systems. It is the extended version of preliminary paper
included in the proceedings of the 2018 American Control Conference.
