  The KP and 2D Toda tau-functions of hypergeometric type that serve as
generating functions for weighted single and double Hurwitz numbers are related
to the topological recursion programme. A graphical representation of such
weighted Hurwitz numbers is given in terms of weighted constellations. The
associated classical and quantum spectral spectral curves are derived, and
these are interpreted combinatorially in terms of the graphical model. The pair
correlators are given a finite Christoffel-Darboux representation and
determinantal expressions are obtained for the multipair correlators. The genus
expansion of the multicurrent correlators is shown to provide generating series
for weighted Hurwitz numbers of fixed ramification profile lengths. The WKB
series for the Baker function is derived and used to deduce the loop equations
and the topological recursion relations in the case of polynomial weight
functions.
