One of the predominant schools of thought in networking today is that monitoring and control of large scale networks is only practical at the edge. With intelligent and adaptive elements at the edge of the network, core devices can function as simple, robust routers. However, the effectiveness of edge-based control can be significantly enhanced by information about the internal network state. If the core is endowed with minimal monitoring and data collection capabilities, then methods for inferring state information from edge-based traffic measurements are of great interest. One of the most fundamental components of the state is the routing topology. The focus of this paper is a new Maximum Likelihood approach to topology identification that makes use only of measurements performed between host computers and requires no special support (e.g., ICMP responses) from internal routers.