Introduction to Complex Networks: Theory and Applications

The modern science of networks has brought significant advances to our understanding of complex systems. Real-world entities are often interconnected with each other through explicit or implicit relationships to form a complex network. Examples of complex networks are found in many fields of science such as biological, technological, economic as well as social systems. In this seminar the speaker will present an introduction to the science of complex networks, starting from the theoretical foundations of graph theory and giving emphasis to representation, analysis and modeling. Also several applications of complex networks to real-world problems and data will be proposed. In particular, the World Trade Web (WTW), as the complex network representation of the international trade system, will be discussed. In this case, several tools and methodologies - recently developed in the framework of network science - can be exploited to extract information from the trading system in order to point out a nontrivial structural organization. As a result a new level of description, that goes beyond the country-specific analyses used in more traditional economic studies of trade, can be obtained, allowing an analysis at the large scale from an interdisciplinary approach. Finally the application of recurrence networks to the analysis of nonlinear dynamical systems will be proposed, together with some open questions for future research.