More and more multimedia streaming is transported in the Internet today, and it occupies a great quantity of network resources. Since many users need to have their data shared among an interesting group, it is important to explore group communication mechanisms. IP multicast is a traditional solution by which the group communication can be implemented. Compared with unicast, it can avoid duplicate transmission in many links, and can save the network bandwidth. But IP multicast can not be implemented in the most of Internet routers for some management and market causes. In another way, P2P group communication has received much attention of many researchers due to its low cost and independence of the technologies used by the network infrastructure.P2P group communication is a complex process. It involves many matters, such as network construction, network maintenance, information distribution, information collection and so on. These matters are associated with each other.While the mode in which an overlay network is constructed governs the choice of the information transmission path, the information distribution policy can suggest the best way in which the overlay network should be established as well. In particular, the overlay topology will shape the traffic distribution pattern, and decides what kind of transmission quality the users can get from the network. The research work of this dissertation is focused on the network topology of P2P group communication. The major contributions of the dissertation are summarized as follows:1.In the light of the characteristics of P2P group communication, we define two graph metrics, RH and RD, to quantify the matching degree between the overlay and the underlay network. Then it is shown that given a topology ? (n, k), for any node in the topology only by choosing randomlyΘ(log n) other nodes to test, can one ensure that the topology will be non-strong connective, and if he chooses ?? 2.997×n0.5312?? other nodes randomly to test, then he can conclude that the length from the source host to any other host will be at most as twice as the diameter of the underlay network. In other words, the RH is equal to 2. The discovery manifests that the non-complete test can achieve the goal of topology discovery instead of a full test. Our simulation shows that the path will not be improved obviously with the further increase of k , when it reaches a certain value. In addition to this, the dissertation shows that when RH=3 and RH=4, the results are similar.2.In regard to the application layer routing of tree-based P2P multicast, the dissertation presents a new kind model of spanning tree, named DCMD, in which the path delay, the