Complex networks are ubiquitous in real word and represent a key model for both human made and natural systems. An important characteristics that distinguishes technological networks from biological networks is the assortativity, i.e. the correlation among the degrees of connected nodes. We apply spectral analysis to investigate how assortativity influences the robustness of a network with respect to failure propagations or epidemic spreading. We find a no free lunch situation: while disassortative networks are more robust since they have a higher failure threshold, in assortative networks there is more time for intervention before total breakdown. © 2013 Springer-Verlag.