  We study discounted Hamilton Jacobi equations on networks, without putting
any restriction on their geometry. Assuming the Hamiltonians continuous and
coercive, we establish a comparison principle and provide representation
formulae for solutions. We follow the approach introduced in 11, namely we
associate to the differential problem on the network, a discrete functional
equation on an abstract underlying graph. We perform some qualitative analysis
and single out a distinguished subset of vertices, called lambda Aubry set,
which shares some properties of the Aubry set for Eikonal equations on compact
manifolds. We finally study the asymptotic behavior of solutions and lambda
Aubry sets as the discount factor lambda becomes infinitesimal.
