We analyze the spreading of viruses in scale-free networks with high clustering and degree correlations, as found in the Internet graph. For the Suscetible-Infected-Susceptible model of epidemics the prevalence undergoes a phase transition at a finite threshold of the transmission probability. Comparing with the absence of a finite threshold in networks with purely random wiring, our result suggests that high clustering and degree correlations protect scale-free networks against the spreading of viruses. We introduce and verify a quantitative description of the epidemic threshold based on the connectivity of the neighborhoods of the hubs.
Eguíluz and Klemm study the spreading of viruses in scale-free networks with large clustering coefficient and degree correlation, which they model as highly clustered scale-free graphs REF .
Epidemic threshold in structured scale-free networks
Phys. Rev. Lett. 89, 108701 (2002)
Physics Biology Medicine