This work presents a method to aid in the prioritization of research within a scientific domain. The domain is encoded into a directed network in which nodes represent factors in the domain, and directed links between nodes represent known or hypothesized causal relationships between the factors. Each link is associated with a numeric weight that indicates the degree of understanding of that hypothesis. Increased understanding of hypotheses is represented by higher weights on links in the network. Research is prioritized by calculating optimal allocations of limited research resources across all links in the network that maximize the degree of overall knowledge of the research domain. We quantify the level of knowledge of individual nodes (factors) in the map by a network centrality measure that reflects in dependencies between knowledge level of nodes and the knowledge level of their parent nodes in the map. We analyzed a funded research proposal concerning the fate and transport of nanomaterials in the environment to illustrate the method.