Complex Networks: Data Analysis, Models, Tools, Applications

We live, as defined by prof. Chua, in the age of complexity, whose ubiquity is the reason of the increasing interest in the scientific community. Many of the systems that surround us are complex. The goal of understanding their properties motivates many researchers. Universal laws and phenomena are essential to inquiry and to understand and all scientific endeavor is based on the existence of universality, which manifests itself in diverse ways. The study of complex systems as a new effort seeks to increase the ability to understand the universality that arises when systems are highly complex. A complex system may be thinked as a system formed out of many components whose behavior is emergent, meaning that the behavior of the system cannot be simply inferred from the behavior of its components. In fact, it is not possible to describe the whole without describing each part, and each part must be described in relation to other parts to understand the behavior of a complex system. The amount of information necessary to describe the behavior of such a system is a measure of its complexity. Usually, the behavior of a complex system is investigated considering how the simple units communicate. Thus, a complex system can be defined by its network of interactions and studied according to graph theory. The aim of this PhD Thesis is to provide new tools and strategies for the analysis and modeling of complex systems. The designed tools will be then applied to two particular classes of complex systems: complex networks and cellular automata. In particular, several fundamental topics of complex networks have been faced in this work. Starting from the key issue of data analysis in networks, which due to the large availability of data has now become a fundamental aspect of the research in complex networks, we found that existing models do not adequately reproduce the characteristics, often uniques, of the social networks analysed and introduced a new model of growing network based on an attachment to communities instead of sparse nodes. We have then considered one of the major applications of complex networks, i.e., power grids. While most of the approaches existing in literature are static ones and focuse on the network topology, we considered a model which explicitely takes into account the oscillatory dynamics of power grid nodes. Our results revealed different qualitative scenarios to the network failure. Finally, the Thesis focuses on a hardware tool for the emulation of a nearest-neighbor coupled network, which, despite its simple topology, is able to generate many complex phenomena and for a set of parameters is equivalent to a Turing machine. The Thesis is organized as follow: in Chapter 1 complex systems and in particular complex networks will be introduced; Chapter 2 and 3 will describe the results obtained on social networks and power grids; Chapter 4 will introduce a new stand-alone complex system hardware emulator; in the conclusive Chapter the conclusions will be drawn.