In this paper, given a network and a subdivision of it, we show how the Group Inverse of the subdivision network can be related to the Group Inverse of initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both networks and takes advantatge on the definition of the Group Inverse matrix.
Carmona, A., Mitjana, M., Monso, E. The group inverse of subdivision networks. "Electronic notes in discrete mathematics", Octubre 2016, vol. 54, p. 295-300.