When k nn (k) increases with k, the network is said to be assortative on the degree; that is, high-degree nodes have a tendency to link to other high degree nodes, a behaviour often observed in social networks. Other types of networks, such as the internet at router level, show the converse behaviour; that is, nodes of high degree tend to link to nodes with low degree [63, 89] . Characterising degree correlations is important for understanding disease spread. The classic example is the existence of strong correlations in sexual networks which were shown to be a key factor in understanding HIV spread [90] . More recently, mean field solutions of the SIS model on networks have shown that both the speed and extent of an epidemic are dependent on the correlation pattern of the substrate network [91, 92] .