Earth to air heat exchanger (EAHE) is a well-known technique used to preheat or precool outdoor air before blowing it into a building. However, its geometry is often very simple as it consists in one or multiple straight pipes, while more complex arrangements can be found in heat exchangers design. In this paper, we explore the advantage of designing an EAHE as a network through the Constructal law point of view. A methodology is first proposed to design a single pipe EAHE when the need is defined in terms of cooling power, overall efficiency and enthalpy difference between the inlet air and the ground. Next, the single pipe EAHE is used as a reference for designing a tree-shaped network under the constraint of identical fluid volume and cooling power. The geometrical features are allowed to change for the different branches of the network. The network coefficient of performance is found to increase significantly with the bifurcation level, illustrating the superior performances of the network. This approach was found to be robust as the improvements were not depending on the cooling demand or the environmental conditions. However, further work is needed to move from this theoretical result to practical considerations.