Shock Diffusion in Regular Networks: The Role of Transitive Cycles

We study how the presence of transitive cycles in the interbank network affects the extent of financial contagion. In a regular network setting, where the same pattern of links repeats for each node, we allow an external shock to propagate losses through the system of linkages (interbank network). The extent of contagion (contagiousness) of the network is measured by the limit of the losses when the initial shock is diffused into an infinitely large network. This measure indicates how a network may or may not facilitate shock diffusion in spite of other external factors. Our analysis highlights two main results. First, contagiousness decreases as the length of the minimal transitive cycle increases, keeping the degree of connectivity (density) constant. Second, as density increases the extent of contagion can decrease or increase, because the addition of new links might decrease the length of the minimal transitive cycle. Our results provide new insights to better understand systemic risk and could be used to build complementary indicators for financial regulation.