In our prior work, the networks that we studied were limited by the computational cost of network analysis, in particular due to the poor scaling of shortest-path graph algorithms. These costs constrained the number of species as well as the number and types of reactions contained in the networks. Even more critically, our prior graph-based analysis approach was limited in its predictive capacity; in order to apply shortest-path algorithms, products of interest had to be known a priori. Here we confront the more challenging problem of exploring a reactive space without significant knowledge of end products. Specifically, we seek to search for many feasible pathways under various starting conditions to a range of products, byproducts, and intermediates, including species that might not be known to be important at the time of network construction.