Many of the systems that surround us, such as road traffic flow, communication networks, densely populated communities, ecosystems with competing species, or the human brain (with neurons), are large, complex, dynamic, and highly nonlinear in their global behaviour. However, over the past 10 years it has been shown that many complex systems exhibit similar topological features in the way their underlying elements are arranged (Albert and Barabási 2002).

Underlying much of the current research is the notion that, in some way, topology affects dynamics that take place on the network, and vice versa. In this chapter I will explore some of the properties of complex social networks.

One of the most well known properties of social networks is the small-world phenomenon. This is something that most of us have experienced. Often we meet people with whom we have little in common, and unexpectedly find that we share a mutual acquaintance. The idea of '6 degrees of separation' is now firmly embedded in folklore, embracing everyone from Kevin Bacon to Monica Lewinsky (Watts 2003). Analysis of social networks has shown that the patterns of interactions that surround each of us, often determines our opportunities, level of influence, social circle, wealth, and even our mental well being.

In this chapter I explore some of the properties of complex social networks. The following section provides a number of examples of complex networks from a range of different contexts. Then, I provide an information theoretic-based approach to detect strong groups in social networks. It is followed by a detailed description of a game theoretic model, in which each of the agents is a decision making unit. This example shows how social network can influence the enforcement of certain behaviours within the system.