The ability to characterize the links on network topology is of great importance in both research and practice. Existing approaches capture only the topology, regardless of many critical link properties such as bandwidth and utilization. We present RichMap, an active probing system, to measure all link available bandwidth on network topology from an arbitrary end node. To do this, RichMap not only needs to discover the complete topology of surrounding networks without any prerequisite, but it also has to capture link available bandwidth by measuring paths in the topology. The accuracy and efficiency of RichMap have been verified through both simulations and network experiments over 12 diverse networks. We analyzed the result of experiments, and found that RichMap is able to accurately and efficiently capture all link available bandwidth when most of the nodes are no more than six links away from the source node.