  We put forward the concept of measure graphs. These are (possibly
uncountable) graphs equipped with an action of a groupoid and a measure
invariant under this action. Examples include finite graphs, periodic graphs,
graphings and percolation graphs. Making use of Connes' non-commutative
integration theory we construct a Zeta function and present a determinant
formula for it. We further introduce a notion of weak convergence of measure
graphs and show that our construction is compatible with it. The approximation
of the Ihara Zeta function via the normalized version on finite graphs in the
sense of Benjamini-Schramm follows as a special case. Our framework not only
unifies corresponding earlier results occurring in the literature. It likewise
provides extensions to rich new classes of objects such as percolation graphs.
