known that any two people are linked by a chain of maybe half a dozen others who are pairwise acquainted – known as the ‘small-world’ phenomenon. This idea was popularised by Milgram in the 60s [@Milgram67]. An explanation started to emerge in 1998 when Watts and Strogatz produced the alpha model. Alpha is a parameter that expresses the tendency of nodes to introduce their neighbours to each other; with $\alpha=0$, each node is connected to its neighbours’ neighbours, so the network is a set of disconnected cliques, while with $\alpha = \infty$, we have a random graph. They discovered that, for critical values of $\alpha$, a small-world network resulted. The alpha model is rather complex to analyse, so they next introduced the beta network: this is constructed by arranging nodes in a ring, each node being connected to its $r$ neighbours on either side, then replacing existing links with random links according to a parameter $\beta$; for $\beta=0$ no links are replaced, and for $\beta=1$ all links have been replaced, so that the network has again become a random graph [@WS98]. The effect is to provide a mix of local and long-distance links that models observed phenomena in social and 