To study signals on networks, to detect epidemics, or to predict blackouts, we need to understand network topology and its impact on the behavior of network processes. The high dimensionality of large networks presents significant analytical and computational challenges; only specific network structures have been studied without approximation. We consider the impact of network topology on the limiting behavior of a dynamical process obeying the stochastic rules of SIS (susceptible-infected-susceptible) epidemics using the scaled SIS process. We introduce the network effect ratio, which captures the preference of individual agents versus the preference of society (i.e., network) and investigate its effects.