Static DHT topologies influence important features of such DHTs such as scalability, communication load balancing, routing efficiency and fault tolerance. Nevertheless, it is commonly recognized that the primary difficulty in designing DHT is not in static DHT topologies, but in the dynamic DHT algorithm which adapts various static DHT topologies to a dynamic network at Internet. As a direct consequence, the DHT community has been paying more attention to the dynamic DHT algorithm design, resulting in a variety of DHT systems lacking of a common view for analysis and interoperation.In this paper we reiterate the importance of static DHT topologies in the DHT system design by analyzing and classifying current DHTs in terms of their static topologies based on a grouptheoretic model: Cayley graphs. We show that most of current DHT proposals use Cayley graphs as static DHT topologies, thus taking advantage of several important Cayley graph properties such as vertex/edge symmetry, decom...