Improved network topology discovery techniques are disclosed. For example, an automated method for discovering a topology of a network, having a plurality of nodes, includes the following steps. A first traceroute process is performed for a given source node and one or more destination nodes listed in a target list so as to discover one or more paths through one or more intermediate nodes between the given source node and the one or more destination nodes. The one or more intermediate nodes discovered during the first traceroute process are added to the target list. A second traceroute process is performed for the given source node and the one or more intermediate nodes discovered during the first traceroute process so as to discover one or more paths through one or more additional intermediate nodes between the given source node and the one or more intermediate nodes discovered during the first traceroute process. When one or more additional intermediate nodes are discovered as a result of performance of the second traceroute process, the one or more additional intermediate nodes are added to the target list and the traceroute process is repeated to determine the existence of any further intermediate nodes. When no new intermediate nodes are discovered as a result of performance of the second traceroute process or a subsequent traceroute process, the nodes in the target list are identified as a target closure set for the given source node.