  We review selected results related to robustness of networked systems in
finite and asymptotically large size regimes, under static and dynamical
settings. In the static setting, within the framework of flow over finite
networks, we discuss the effect of physical constraints on robustness to loss
in link capacities. In the dynamical setting, we review several settings in
which small gain type analysis provides tight robustness guarantees for linear
dynamics over finite networks towards worst-case and stochastic disturbances.
We also discuss network flow dynamic settings where nonlinear techniques
facilitate in understanding the effect on robustness of constraints on capacity
and information, substituting information with control action, and cascading
failure. We also contrast the latter with a representative contagion model. For
asymptotically large networks, we discuss the role of network properties in
connecting microscopic shocks to emergent macroscopic fluctuations under linear
dynamics as well as for economic networks at equilibrium. Through the review of
these results, the paper aims to achieve two objectives. First, to highlight
selected settings in which the role of interconnectivity structure of a network
on its robustness is well-understood. Second, to highlight a few additional
settings in which existing system theoretic tools give tight robustness
guarantees, and which are also appropriate avenues for future network-theoretic
investigations.
