  Scharlemann and Thompson define the width of a 3-manifold M as a notion of
complexity based on the topology of M. Their original definition had the
property that the adjacency relation on handles gave a linear order on handles,
but here we consider a more general definition due to Saito, Scharlemann and
Schultens, in which the adjacency relation on handles may give an arbitrary
graph. We show that for compact hyperbolic 3-manifolds, this is linearly
related to a notion of metric complexity, based on the areas of level sets of
Morse functions to graphs, which we call Gromov area.
