In the case of large epidemics and small values of the contact-tracing rate, contact tracing is more effective on assortatively mixed networks than on disassortative mixed networks, although the difference is small. Here, on the assortatively mixed networks, the early, global depletion of highly connected nodes results in a rapid increase in the proportion of susceptible nodes that are poorly connected nodes, and thus are less likely to become infected. For smaller values of the final epidemic size, the epidemics die out earlier and the depletion of susceptible nodes is less important. The efficacy of contact tracing in this case is determined by the more resilient nature of the assortatively mixed networks to the removal of potentially infectious links through tracing. In the case of singlestep versus multi-step contact tracing, the differences are more marked for assortatively mixed networks and small epidemics.