A celebrated theorem of Raynaud describes how to calculate the component group of the special fiber of the N’eron model of the Jacobian of a curve $X$ from the incidence graph of a semistable regular model of $X$. In Baker-Norine’s language of divisors on graphs, Raynaud’s theorem can be translated into a compatibility between the skeleton of the Jacobian of $X$, which is identified with the component group, with the Jacobian of the skeleton of $X$, viewed as a graph. We show how this theorem can be extended to fields with arbitrary (not necessarily discretely valued) rank-1 valuations and metric graphs. As an application we prove that the specialization map from the group of principal divisors of $X$ to the group of principal divisors on its skeleton is surjective, along with the related fact that any rational function on the skeleton is the restriction of the valuation of a rational function $f$ on $X$; this is a powerful analytic tool for constructing rational functions on $X$. We also remark that our formulation of Raynaud’s theorem is functorial in $X$. This work is joint with Matt Baker.