Abrupt transition in the structural formation of interconnected networks

Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent 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 in. Here we show that the composition of independent networks into an interconnected network of networks undergoes a structurally sharp transition as the interconnections are formed. Depending of the relative importance of inter and intra-layer connections, we find that the entire interdependent system can be tuned between two regimes: in one regime, the various layers are structurally decoupled and they act as independent entities; in the other regime, network layers are indistinguishable and the whole system behave 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 that may reflect in new dynamical properties.