We introduce distance entropy as a measure of homogeneity in the distribution
of path lengths between a given node and its neighbours in a complex network.
Distance entropy defines a new centrality measure whose properties are
investigated for a variety of synthetic network models. By coupling distance
entropy information with closeness centrality, we introduce a network
cartography which allows one to reduce the degeneracy of ranking based on
closeness alone. We apply this methodology to the empirical multiplex lexical
network encoding the linguistic relationships known to English speaking
toddlers. We show that the distance entropy cartography better predicts how
children learn words compared to closeness centrality. Our results highlight
the importance of distance entropy for gaining insights from distance patterns
in complex networks.Comment: 11 page