The Sombor-type indices, recently introduced by Gutman, are novel the vertex-degree-based topological indices. Based on these, we study the Sombor-type indices and other new vertex-degree-based topological indices for butterfly networks, augmented butterfly networks, enhanced butterfly networks, Benes networks, mesh derived networks and the Optical Transpose Interconnection System (OTIS) networks, which provide a new kind of prediction indices for these networks.