Abstract: At present, a lot of researchers have focused on semantic overlay network's construction for improving query efficiency in P2P networks.But the research on optimal scale of semantic overlay network is lacked. This paper tried to use mathematic method to model the semantic overlay network. And then model solution method of properties which impacts the routing arithmetic was researched. At the same time, the relationship between semantic overlay network's scale and the capability properties of routing arithmetic was analyzed. In the base of this, the optimal scale of the community would appeare, which supports the construction and research on semantic overlay network effectively.

Key words: Peer-to-peer, Semantic overlay network, Community scale, Mathematic analysis