Scale-Free and Hierarchical Structures in Complex Networks

Networks with complex topology describe systems as diverse as the cell or the World Wide Web. The emergence of these networks is driven by self-organizing processes that are governed by simple but generic laws. In the last three years it became clear that many complex networks, such as the Internet, the cell, or the world wide web, share the same large-scale topology. Here we review recent advances in the characterization of complex networks, focusing the emergence of the scale-free and the hierarchical architecture. We also present empirical results to demonstrate that the scale-free and the hierarchical property are shared by a wide range of complex networks. Finally, we discuss the impact of the network topology on our ability to stop the spread of viruses in complex networks.