  We show that the Voronoi cells of the lattice of integer flows of a finite
connected graph $G$ in the quadratic vector space of real valued flows have the
following very precise combinatorics: the face poset of a Voronoi cell is
isomorphic to the poset of strongly connected orientations of subgraphs of $G$.
This confirms a conjecture of Caporaso and Viviani {Torelli Theorem For Graphs
and Tropical Curves, Duke Math. J. 153(1) (2010), 129-171}.
