A very interesting research on Robustness and assortativity for diffusion-like processes in scale-free networks (PDF) confirmed previous findings (Newman 2002) that the networks where the nodes tend to connect to the nodes with the higher degree (so-called assortative networks) are much more susceptible to epidemic contagion than disassortative networks (where nodes mix in a more heterogeneous fashion).

It has also been shown that one of the more efficient immunization strategies is to focus on the hubs (the most connected nodes), as well as introducing a certain degree of disassortativity in the network’s topology (encouraging periphery members to connect to each other). The abstract of the paper is below:

By analysing the diffusive dynamics of epidemics and of distress in complex networks, we study the effect of the assortativity on the robustness of the networks. We first determine by spectral analysis the thresholds above which epidemics/failures can spread; we then calculate the slowest diffusional times. Our results shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize, while in assortative networks there is a longer time for intervention before epidemic/failure spreads. Moreover, we study by computer simulations the sandpile cascade model, a diffusive model of distress propagation (financial contagion). We show that, while assortative networks are more prone to the propagation of epidemic/failures, degree-targeted immunization policies increases their resilience to systemic risk.