Degree design of coupled infrastructures

A recent asymptotic model of cascading failure in two-domain, coupled infrastructure systems is used to pose and solve a generic degree-distribution design problem. A low-order nonlinear analysis exposes the mechanisms by which optimized graphs can form star-like clusters, as embedded into specialized distributions. Several other design rules are developed. Through examples on coupled systems of finite size, we demonstrate that the main assumption of degree independence can be somewhat relaxed, which is significant for the case of geometric connectivity. A heuristic rule that matches degrees across the domain boundary can offer benefits in most cases.