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.
Type
Thesis, PhD Doctor of Philosophy
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