This paper studies a model for the optimal control of pollution diffusion over time and space by a centralized economic agent. The controls are the investments in two types of production: a less polluting (”green”) technology and a more polluting (”brown”) one. The goal is to maximize an intertemporal utility function which takes into account the cost of pollution. The main novelty is the fact that the spatial component has a network structure. Moreover, in such a time-space setting, we analyze the trade-off between the use of green and brown technologies: this is also a novelty in such a setting. Extending methods from previous works, we can explicitly solve the problem in the case of strictly convex or linear pollution costs.