Network elucidation is the problem of inferring all parameters of a network from a subset of those parameters. We introduce the Network Elucidation Template (NET), which provides a framework upon which algorithms for such problems can be built. NET algorithms take advantage of novel methods for collaboration between human operators and computers. They use visualizations of the peculiar structures that appear in optimal solutions to aid the parameter search. By design, NET is at a high enough level of abstraction to describe a class of algorithms, as opposed to a single algorithm. Given a problem, and the structure of that problem, an effective instantiation of the template into an algorithm can be created. We describe one such instantiation: using a network flow framework to implement a NET algorithm for uncovering smuggling networks; as well as the general template.