This paper proposes several novel hierarchical interconnection networks based on the (3, 3)-graphs, namely folded (3, 3)-networks, root-folded (3, 3)-networks, recursively expanded (3, 3)-networks, and flooded (3, 3)-networks. Just as the hypercubes, CCC, Peterson-based networks, and Heawood-based networks, these hierarchical networks have the following nice properties: regular topology, high scalability, and small diameters. Due to these important properties, these hierarchical networks seem to have the potential as alternatives for the future interconnection structures of multicomputer systems, especially massively parallel processors (MPPs). Furthermore, this paper will present the routing and broadcasting algorithms for these proposed networks to demonstrate that these algorithms are as elegant as the algorithms for hypercubes, CCC, and Petersen- or Heawood-based networks.