  The lattice of integer flows of a graph is known to determine the graph up to
2-isomorphism (work of Su--Wagner and Caporaso--Viviani). In this paper we give
an algorithmic construction of the graphic matroid $\calM(G)$ of a graph $G$,
given its lattice of integer flows $\calF(G)$. The algorithm can then be
applied to compute any other 2-isomorphism invariants (that is, matroid
invariants) of $G$ from $\calF(G)$. Our method is based on a result of Amini
which describes the relationship between the geometry of the Voronoi cell of
$\calF(G)$ and the structure of $G$.
