  We explore the differential geometry of finite sets where the differential
structure is given by a quiver rather than as more usual by a graph. In the
finite group case we show that the data for such a differential calculus is
described by certain Hopf quiver data as familiar in the context of path
algebras. We explore a duality between geometry on the function algebra vs
geometry on the group algebra, i.e. on the dual Hopf algebra, illustrated by
the noncommutative Riemannian geometry of the group algebra of $S_3$. We show
how quiver geometries arise naturally in the context of quantum principal
bundles. We provide a formulation of bimodule Riemannian geometry for quantum
metrics on a quiver, with a fully worked example on 2 points; in the quiver
case, metric data assigns matrices not real numbers to the edges of a graph.
The paper builds on the general theory in our previous work.
