We extend the celebrated result by Lions, Papanicolaou and Varadhan (1987) on the homogenization of Hamilton-Jacobi equation to the network setting. Roughly speaking, we aim at describing the macroscopic behavior of solutions to time dependent Hamilton-Jacobi equations posed on periodic networks by averaging over their microscopic oscillations and neglecting their local features. This is done using a variational approach which relies on the Aubry-Mather theory, namely the study of curves or probability measures that minimize the Lagrangian action. This is a joint work with Antonio Siconolfi and Alfonso Sorrentino.