Invariant d'Hermite du réseau des flots entiers d'un graphe pondéré

To any weighted graph of first Betti number b is naturally associated a lattice of dimension b : the lattice of integral flows. We give here an upper bound of the Hermite invariant of such a lattice in terms of b of order lnb. This order is optimal: it is realized by the Hermite invariant of the lattice of integral flows associated to a systolically economic graph.