Statistical properties of complex networks
Prof. Romualdo Pastor-Satorras
Universitat Politècnica de Catalunya, Barcelona, Spain
15 hours, 4 credits
March 16 - March 18, 2009
Area della Ricerca di Pisa, National Research Council, via G. Moruzzi 1, Pisa, room 7, entrance 3
Contacts: Prof. Luciano Lenzini
This activity is part of the Pisa International School on the Next Generation Internet.
Aims
Many large natural, social, and technological systems can be succesfully described within a unified formalism that combines elements of graph theory and statistical physics. This formalism has been developed in the last years, and has already matured to become the so-called science of complex networks. In this series of lessons we will provide an introduction to the field of complex networks, covering the three main aspects (description, modelling and dynamics) in which it is usually divided.
Outline
Structure and function of complex networks
In this section we will introduce the basic concepts that allow to describe physical systems in terms of complex networks, and how to obtain topological information on those networks at a statistical level. As a paradigmatic example, we will consider in particular the case of the Internet.
Modelling complex networks
Most of the networks observed in nature and technology share as a common feature a scale-free nature, characterized by the presence a power-law distributions. Due to this ubiquitiy of power-laws, some basic models have been proposed, aimed at understanding their origin. In this section we will review this class of scale-free network models.