with the first moment, k , being the average degree, the second, k 2 allowing us to calculate the variance k 2 − k 2 , and so on. The degree distribution is one of the most important ways of characterising a network as it naturally captures the heterogeneity in individuals' potential to become infected as well as cause further infection. Intuitively, the higher the number of edges a node has, the more likely it is to be a neighbour of an already infected node. Also, the more neighbours a node has, the more likely it is to cause a large number of onward cases. Thus, knowing the form of P(k) is crucial for the understanding of the spread of disease. In random networks of the type studied by Erdös and Rényi, P(k) follows a binomial distribution, which is effectively Poisson in the case of large networks. Most real social networks have distributions that are significantly different from the random case.