The topological properties of Peer-to-Peer (P2P) overlay networks are critical factors that dominate the performance of these systems. The P2P networks need a topology with arbitrary size and degree, while the Kautz digraph is a topology with good properties such as constant degree and optimal network diameter O(log_d n). In this paper, We describe that KZCAN is a navel P2P network with constant expected degree. It is based on an overlay network preserving Kautz digraph connections dynamically, and on a distributed hash table (DHT) supporting efficient publish and search procedures. KZCAN shows that the DHT scheme with constant expected degree and can achieve log_{d}(n/(d+1))+1 diameter. The routing length of KZCAN is shorter than CAN or D2B with the same degree when the P2P network is large scale.