Accurate and up-to-date knowledge of topology serves as the basis of a number of network management functions, such as performance monitoring and evaluation, fault detection and location, resource allocation and etc. In this paper, the topology of a switched Ethernet, the most prevalent kind of connection layouts of LANs, is abstracted to a tree and the connection relationships between the network nodes are determined as lineal connections and collateral connections. A set of theorems to determine the nodes' relationships is also presented. Based on the above theorems, a new algorithm for physical topology discovery is proposed, which can construct the whole topology utilizing the incomplete AFTs (address forwarding tables). As an important part of a community broadband integrated services network management system (CBISNMS), this mechanism is working successfully.