  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.
