In previous works the group inverse of a network obtained by some perturbations, as the deletion of a vertex, the addition of a new vertex, contraction of an edge, etc. is obtained in terms of the group inverse of the original network. In this work, two given networks are connected with some edges and the group inverse of the new network is obtained from the group inverse of the two original networks. In particular, the formula for the connection of two networks by just one edge is obtained, and besides the formula for the Kirchhoff index of this kind of networks is given.