  We construct and study a class of spectral graph wavelets by analogy with
Hermitian wavelets on the real line. We provide a localization result that
significantly improves upon those previously available, enabling application to
highly non-sparse, even complete, weighted graphs. We then define a new measure
of importance of a node within a network called the Maximum Diffusion Time, and
conclude by establishing an equivalence between the maximum diffusion time and
information centrality, thus suggesting applications to quantifying
hierarchical and distributed leadership structures in groups of interacting
agents.
