  For the class of noisy time-delay linear consensus networks, we obtain
explicit formulas for risk of large fluctuations of a scalar observable as a
function of Laplacian spectrum and its eigenvectors. It is shown that there is
an intrinsic tradeoff between risk and effective resistance of the underlying
coupling graph of the network. The main implication is that increasing network
connectivity, increases the risk of large fluctuations. For vector-valued
observables, we obtain computationally tractable lower and upper bounds for
joint risk measures. Then, we study behavior of risk measures for networks with
specific graph topologies and show how risk scales with network size.
