We are motivated by the problem of designing a simple distributed algorithm for Peer-to-Peer streaming applications that can achieve high throughput and low delay, while allowing the neighbor set maintained by each peer to be small. While previous works have mostly used tree structures, our algorithm constructs multiple random directed Hamilton cycles and disseminates content over the superposed graph of the cycles. Compared with the algorithms constructing trees, the complexity to dynamically update the network topology in response to peer churn does not increase with the network size under our algorithm. We show that it is possible to achieve the maximum streaming capacity even when each peer only transmits to and receives from Θ(1) neighbors. Further, we show that the proposed algorithm achieves the streaming delay of Θ(logN) when the streaming rate is less than (1 - 1/K) of the maximum capacity for any fixed constant K ≥ 2.