Computer Laboratory, University of Cambridge

1st Mini-Course on Structure and Dynamics of Complex Networks

Lecturer: Vito Latora

Physics Department, University of Catania, Italy


“What do metabolic pathways, ecosystems, the World Wide Web, and propagation of HIV have in common? Until a few years ago, the answer would have been ``very little'': the first two examples are biological and shaped by evolution, the third is a human creation, and the fourth is a mixture of biology and sociological components.  However, in the last few years the answer that has emerged is that these systems all share similar network architectures.  Seemingly out of nowhere, in the span of a few years, network theory has become one of the most visible pieces of the body of knowledge that can be applied to the description, analysis, and understanding of complex systems. New applications are developed at an ever-increasing rate and the promise for future growth is high. Complex networks is now an essential ingredient in the background of any scientist ''

L.A.N. Amaral and J.M. Ottino,  EPJ B, 2004

This minicourse is for graduate and advanced undergraduate students in physics, enginnering, mathematics, biology and computer science, who wants to learn the major ideas developed and the results recently achieved in one of the newest and hottest interdisciplinary research fields. The student will find the main concepts presented in a language which is accessible to a non specialist. He will learn the basic methods of network theory, statistics, nonlinear dynamics and computer science, that allows him to study the structure and the dynamics of complex networks.

The course is a short version (6 lectures of 3 hours each) of a course which has been taught by Vito Latora in the last few years at Scuola Superiore di Catania and at the Physics Department of Università di Catania, Italy.  The minicourse is divided into two parts.  The first part is devoted to the characterization of the structural properties of real world networks, and to the development of new network models. It contains topics of graph theory, social networks analysis, statistical physics, molecular biology, urban planning. The  second part is on the study of different kinds of dynamical processes that take place over a network. Special emphasis is given to percolation and network tolerance to errors and external attacks, random walks and searching, and to the diffusion of infectious diseases in a population. In each of the two parts, the theory is supplemented with examples and applications.