Knowledge creation and dissemination in science and technology systems are perceived as prerequisites for socioeconomic development. The efficiency of creating new knowledge is considered to have a geographical component, that is, some regions are more capable in terms of scientific knowledge production than others. This article presents a method of using a network representation of scientific interaction to assess the relative efficiency of regions with diverse boundaries in channeling knowledge through a science system. In a first step, a weighted aggregate of the betweenness centrality is produced from empirical data (aggregation). The subsequent randomization of this empirical network produces the necessary null model for significance testing and normalization (randomization). This step is repeated to provide greater confidence about the results (re-sampling). The results are robust estimates for the relative regional efficiency of brokering knowledge, which is discussed along with cross-sectional and longitudinal empirical examples. The network representation acts as a straightforward metaphor of conceptual ideas from economic geography and neighboring disciplines. However, the procedure is not limited to centrality measures, nor is it limited to geographical aggregates. Therefore, it offers a wide range of applications for scientometrics and beyond.