Disentangling shock diffusion on complex networks: identification through graph planarity

Large scale networks delineating collective dynamics often exhibit cascading failures across nodes leading to a system-wide collapse. Prominent examples of such phenomena would include collapse on financial and economic networks. Intertwined nature of the dynamics of nodes in such network makes it difficult to disentangle the source and destination of a shock that percolates through the network, a property known as reflexivity. In this article, a novel methodology is proposed which combines vector autoregression model with an unique identification restrictions obtained from the topological structure of the network to uniquely characterize cascades. In particular, we show that planarity of the network allows us to statistically estimate a dynamical process consistent with the observed network and thereby uniquely identify a path for shock propagation from any chosen epicenter to all other nodes in the network. We analyze the distress propagation mechanism in closed loops giving rise to a detailed picture of the effect of feedback loops in transmitting shocks. We show usefulness and applications of the algorithm in two networks with dynamics at different time-scales: worldwide GDP growth network and stock network. In both cases, we observe that the model predicts the impact of the shocks emanating from the US would be concentrated within the cluster of developed countries and the developing countries show very muted response, which is consistent with empirical observations over the past decade.