— The topological properties of peer-to-peer overlay networks are critical factors that dominate the performance of these systems. Several non-constant and constant degree interconnection networks have been used as topologies of many peerto-peer networks. One of these has many desirable properties: the Kautz digraph. Unlike interconnection networks, peer-to-peer networks need a topology with an arbitrary size and degree, but the complete Kautz digraph does not possess these properties. In this paper, we propose Moore: the first effective and practical peer-to-peer network based on the incomplete Kautz digraph with O(logd N) diameter and constant degree under a dynamic environment. The diameter and average routing path length are logd(N) − logd(1 + 1/d) and logd N, respectively, and are shorter than that of CAN, butterfly, and cube-connected-cycle. They are close to that of complete de Bruijn and Kautz digraphs. The message cost of node joining and departing operations are at most...