### Complex Networks - Introduction

F. A. Rodrigues, P. R. Villas Boas, G. Travieso and L. da F. Costa

Complex Networks are everywhere. Many phenomena in nature can be modeled as a network, as brain structures, protein-protein interaction networks, social interactions and the Internet and WWW. All such systems can be represented in terms of nodes and edges indicating connections between nodes. In Internet, for example, the nodes represent routers and the edges the physical connections between them. In the same way, in transport networks, the nodes can represent the cities and the edges the highways that connect them. These edges can have weights, which can represent the flux of car in a highway or a frequency of interactions between two words in a language network.

An important characteristic of these networks is that they are not random, but have a more structured architecture. The topology of different networks, as protein-protein interaction networks and Internet, for example, are very close: they follow the power law, exhibiting a scale free structure. So, an important question is raised: How can systems as fundamentally different as cells and the Internet have the same underlying topological features? Finding the fundamental laws which generate these networks, modeling and characterizing them are the current challenges in complex network research.

In this site we provide some resources for the study of complex networks. For those who want to start in this interesting new field of science, we recommend the paper of Barabási and Boneabeau, published in Scientific American in 2003, and the surveys as a first step. Books about complex networks, as Linked and Networks: From biological nets to the Internet and WWW, are also good starting points.

University of São Paulo - USP

Institute of Physics at São Carlos - IFSC

Brazil