Volumes on Tropical Jacobians

We begin by discussing the Wirtinger formula from classical complex geometry, and its consequence on volumes of complex submanifolds.  We then show that an analogous formula in the case of metric graphs and its Jacobian in combination with Lagerberg's \$p,q\$-forms yields a formula for volume of \$W_{d}\$ the image of \$d\$-fold powers of the metric graph in its Jacobian.