A Tipping Point in the Structural Formation of Interconnected Networks

Abstract

The interaction substrate of many natural and synthetic systems is well represented by a complex mesh of networks where information, people and energy flows. These networks are interconnected with each other, and present structural and dynamical features different from those observed in isolated networks. While examples of such dissimilar properties are becoming more abundant, for example diffusion, robustness and competition, it is not yet clear where these differences are rooted. Here we show that the composition of independent networks into an interconnected network of networks undergoes a structurally sharp transition, a tipping point, as the interconnections are formed. Depending on the relative importance of inter-and intra-layer connections, we find that the entire interconnected system can be tuned between two regimes: in one regime, the various layers are structurally decoupled and they act essentially as independent entities; in the other regime, strong structural correlation arise, and network layers are indistinguishable i.e. the whole system behaves as a single-level network. We analytically show that the transition between the two regimes is discontinuous even for finite size networks. Thus, any real-world interconnected system is potentially at risk of abrupt changes in its structure, which may manifest new dynamical properties.