I will present joint work with Michael Groechenig, which associates a degenerating family of abelian varieties to a graph. On the one hand, it is an algebraisation of the `Dolbeault’ hypertoric spaces originally defined by Hausel and Proudfoot. On the other, it is an approximation to the relative compactified Jacobian of a family of curves degenerating to a nodal curve with specified dual graph. We then consider our construction over the p-adic numbers, and compute the p-adic volumes of the fibers. We find they are given by the Kirchoff polynomial of the graph.

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