Introduction to the theory of complex networks

Abstract

There was a new direction of studying of the complex systems last years, considering them as networks. Nodes in such networks represent elements of these complex systems, and links between nodes - interactions between elements. These researches deal with real systems, such as biological (metabolic networks of cells, functional networks of a brain, ecological systems), technical (the Internet, WWW, networks of the companies of cellular communication, power grids), social (networks of scientific cooperation, a network of movie actors, a network of acquaintances). It has appeared that these networks have more complex architecture, than classical random networks. In the offered review the basic concepts theory of complex networks are given, and the basic directions of studying of real networks structures are also briefly described.

Keywords

• small-world phenomenon
• scale-free networks
• assortativity
• cascading failures