The function Li n ðxÞ is the nth polylogarithm of x and acts as a normalizing constant. The exponential cut-off of the scale-free distribution is determined by K. Following Newman (2003a), a value of gZ2.5 is used for the power-law exponent. The network analysis that illustrates the effect of preferential mixing is performed for KZ100. For this value of K, the average number of connections per node in the networks is hkiz1.7. To explore a range of parameter values that support meaningful epidemics (i.e. where the epidemic is large enough to be of a significant public health concern), hki must be sufficiently large to allow for a range of new infections in the first generation well above 1. Therefore, the networks are generated by only accepting nodes with kR3 (see Kiss et al. 2006b ). Moreno et al. (2003) proposed a numerical method for epidemic models that can account for connectivity correlations. While this method works without explicitly generating the network, it offers less flexibility when considering disassortatively mixed networks. Here, we use epidemic simulations on networks with NZ10 000 nodes and consider values of rZK0.2, K0.10, K0.05 for disassortatively mixed networks and rZ0.05, 0.10, 0.2 for assortatively mixed networks. The limits are chosen as the values over which the algorithm appears to be robust (M. E. J. Newman 2006, personal communication) ; this range of r values is sufficient to give marked differences in the epidemic threshold for the transmission rate, number of nodes traced, final epidemic size and to illustrate important trends in contact-tracing efficacy. A further check on the mixing pattern is illustrated in the electronic supplementary material by a plot of the average connectivity of a neighbour as a function of node connectivity for different values of r.