  We provide a Lax-Oleinik-type representation formula for solutions of
time-dependent Hamilton-Jacobi equations, posed on a network with a rather
general geometry, under standard assumptions on the Hamiltonians. It depends on
a given initial datum at $t=0$ and a flux limiter at the vertices, which both
have to be assigned in order the problem to be uniquely solved. Previous
results in the same direction are solely in the frame of junction, namely
network with a single vertex. An important step to get the result is to define
a suitable action functional and prove existence as well as
Lipschitz-continuity of minimizers between two fixed points of the network in a
given time, despite the fact that the integrand lacks convexity at the
vertices.
