Live peer-to-peer (P2P) streaming applications have been successfully deployed in the Internet. With relatively simple peer selection protocol design, modern live P2P streaming applications are able to provide millions of concurrent users adequately satisfying viewing experiences. That said, few existing research has provided sufficient insights on the time-varying internal characteristics of P2P topologies in live streaming. With 120 GB worth of traces in late 2006 from a commercial P2P live streaming system of UUSee Inc. in Beijing, this paper represents the first attempt in the research community to explore topological properties in practical P2P streaming, and how they behave over time. Starting from classical graph metrics, such as degree, clustering coefficient, and reciprocity, we explore and extend them in specific perspectives of streaming applications. We also compare our findings with existing insights from topological studies of P2P file sharing applications, which s...