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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.