Coupled complex networks : structure, adaptation and processes

Abstract

In the last 15 years, network science has established itself as a leading scientific tool for the study of complex systems, describing how components in a system interact with one another. Understanding the structure and dynamics of these networks of interactions is the key to understanding the global behaviour of the systems they represent, with a wide range of applications to fundamental societal problems; from designing stable and resilient infrastructures which are critical to our sustainability, to identifying topological patterns in interactome networks that are associated with breast cancer. Most studies so far have focused on isolated single networks that do not interact with or depend upon other networks, while in reality networks rarely live in isolation and are often just one component in a much larger complex multilevel network. Together with the increased availability of richer, bigger and multi-relational datasets, the analysis of coupled networks has been recently attracting many researchers, and has exposed a multitude of new features and phenomena that were not observed for isolated networks. In this thesis, we present analytical, numerical and empirical studies of coupled complex networks, aiming to understand the implications of coupling to the functionality and behaviour of complex systems. First, we present a theoretical framework for studying the robustness of modular or interconnected networks, providing the critical concentration of interconnections between modules, above which the internal structure of each module is inseparable from the system as a whole. Second, we present another theoretical framework to study epidemic spreading in interconnected adaptive networks, discovering a new stationary state that only emerges in the case of weakly coupled networks, where the epidemic localise in the coupled nodes. In order to obtain the exact quantitative behavior of the new state from the analytical model, one must account for the actual second-order moments of the system, even for homogeneous networks, where in single networks it is usually sufficient to treat such higher-order terms by a uniform approximation. Thirdly, we present a numerical study on the effect of correlated coupling on spreading dynamics in the presence of resource constraints, finding that positive correlation between coupled nodes can impede flow process through contention, and thus constitute a less spreading-efficient structure than negatively correlated networks. Finally, we complete the thesis with a large-scale empirical study of interacting transportation networks in the entire metropolitan areas of both London and New York. We find that coupling can strongly affect the structure, and consequently the behaviour, of such multilayer transportation systems.