Least susceptible networks to systemic risk

Abstract

There is empirical evidence that as the connectivity of a network increases, there is an increase in the network performance, but at the same time, there is an increase in the chance of risk contagion which is extremely large. If external shocks or excess loads at some agents are propagated to the other connected agents due to failure, the domino effects often come with disastrous consequences. In this paper, we design the least susceptible network to systemic risk. We consider the threshold-based cascade model, proposed by Watts [13]. We propose the network design model in which the associated adjacency matrix has the largest maximum eigenvalue. The topology of such a network is characterized as a core-periphery structures that consists of a partial complete graph of hub nodes and stub nodes that are connected to one of the hub nodes. The introduced network can reduce the turbulence of shocks triggered and prevent the spread of systemic risk. By both mathematical analysis and agent-based simulations, we show that the slightly differences of the structure of network causes systemic risk.