Interplays Between Systemic Risk and Network Topology in Consensus Networks

Abstract: We consider a few notions of systemic risk measures in first-order time-invariant linear dynamic networks steered by additive noise. We establish connections between the risk measures, the connectivity properties of the communication graph and eventually the performance measure of these networks. Double inequalities are derived that bound the systemic risk measures in terms of spectral properties of the underlying graph of the network. We demonstrate that in an agreement seeking network, strengthening connectivity, decreases the risk of systemic events up to a lower limit, while in a sensor placement protocol, the possibility of systemic event can increase proportionally connectivity-which hints on emergence of an intrinsic interplay between risk and network topology.