Degree design of coupled infrastructures

Abstract

A recent asymptotic model of cascading failure in two-domain, coupled infrastructures is used to pose and solve a specific degree-distribution design problem. Low-order non-linear analysis exposes the mechanisms by which optimised graphs can form star-like clusters, and suggests why the optimisation is well-behaved numerically. Through computational examples on coupled systems of finite size, we demonstrate that the model assumption of degree independence can be somewhat relaxed, which is significant for geometric connectivity. Further, an assortative heuristic rule that matches degrees across the domain boundary can offer benefits in most finite-size cases.