From social networks to large scale critical infrastructure, the systems that surround us are large and complex. Despite their obvious differences these systems share a number of common regularities—such as the small world properties. In this chapter we have reviewed some recent work on the structure and function of networked systems. Work in this area has been motivated to a high degree by empirical studies of real-world networks such as the Internet, the World Wide Web, social networks, collaboration networks, citation networks and a variety of biological networks. We have reviewed these empirical studies, focusing on a number of statistical properties of networks that have received particular attention, including path lengths, degree distributions, and clustering. Moving beyond these statistical regularities, the structure and nature of the interactions between the elements within a system can provide insights into the dynamics taking place in the network and as well as the way the network is being shaped by the dynamics.

In this chapter I have explored several notions. First, by understanding the nature of the interaction between players of chess we can extract dominance hierarchies. These hierarchies can be examined through time to gain an understanding as to how the system evolves, in this case, how the dynamics affect the topology. I also explored how the structure of a network affects the dynamics taking place upon it and showed that the regularities we see in social systems may be a consequence of the dynamics taking place. These regularities are also echoed across other types of social systems, suggesting universal laws of organisation.

In looking forward to future developments in this area, it is clear that there is much to be done. The study of complex networks is still in its infancy. Several general areas stand out as promising for future research. First, while we are beginning to understand some of the patterns and statistical regularities in the structure of real world networks, our techniques for analysing networks are, at present, no more than a grab-bag of miscellaneous and largely unrelated tools (Newman 2003). We do not yet, as in some other fields, have a systematic program for characterising network structure. We need a systematic framework by which we can analyse complex networks in order to identify key dynamical and structural properties. Second, there is much to be done in developing models of networks, both to help us understand network topology and to act as a substrate for the study of processes taking place on networks (Watts and Strogatz 1998; Newman 2003). Finally, and perhaps the most important direction for future study, is the behaviour of processes taking place on networks. The work describing the interplay between social structure and game theoretic decision making is only a timid first attempt at describing such processes, and yet this, in a sense, is the ultimate goal in the field: to understand the behaviour of the network systems that surround us.