We propose a taxonomy of botnet structures, based on their utility to the botmaster. We propose key metrics to measure their utility for various activities (e.g., spam, ddos). Using these performance metrics, we consider the ability of different response techniques to degrade or dis- rupt botnets. In particular, our models show that targeted responses are particularly effective against scale free botnets and ef- forts to increase the robustness of scale free networks comes at a cost of diminished transitivity. Botmasters do not ap- pear to have any structural solutions to this problem in scale free networks. We also show that random graph bot- nets (e.g., those using P2P formations) are highly resistant to both random and targeted responses. We evaluate the impact of responses on different topolo- gies using simulation and demonstrate the utility of our pro- posed metrics by performing novel measurements of a P2P network. Our analysis shows how botnets may be classified according to structure and given rank or priority using our proposed metrics. This may help direct responses and sug- gests which general remediation strategies are more likely to succeed.