  To any weighted graph of first Betti number b is naturally associated a
lattice of dimension b, definite in a similar way that the jacobian for a
Riemann surface. This class of lattices generated by graphs is particularly
interesting. We show here an upperbound of the Hermite invariant of such a
lattice according to b whose order is ln b. This order is optimal : it is
realized by the Hermite invariant of the jacobian of a systolicly economic
graph.
