  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.
