Centrality, in some sense, captures the extent to which a vertex controls the flow of information in a network. Here, we propose Local Detour Centrality as a novel centrality-based betweenness measure that captures the extent to which a vertex shortens paths between neighboring vertices as compared to alternative paths. After presenting our measure, we demonstrate empirically that it differs from other leading central measures, such as betweenness, degree, closeness, and the number of triangles. Through an empirical case study, we provide a possible interpretation for Local Detour Centrality as a measure that captures the extent to which a word is characterized by contextual diversity within a semantic network. We then examine the relationship between our measure and the accessibility to knowledge stored in memory. To do so, we show that words that occur in several different and distinct contexts are significantly more effective in facilitating the retrieval of subsequent words than are words that lack this contextual diversity. Contextually diverse words themselves, however, are not retrieved significantly faster than non-contextually diverse words. These results were obtained for a serial semantic memory task, where the word’s location constitutes a significant mediator in the relationship between the proposed measure and accessibility to knowledge stored in memory.