General Biswapped Networks and Their Topological Properties

In the paper, we propose a new systematic model, called General Biswapped Networks (GBSNs), to construct hierarchical interconnection networks that are able to maintain many desirable attributes of the underlying basis networks consisting of clusters. The model is inspired by and extended from Biswapped Networks (BSNs) and OTIS networks. A network in the new proposed model Gbsw(Ω, Δ) is composed of m copies of some n-node basis network Ω and n copies of some m-node basis network Δ. Such a network uses a simple rule for connectivity that ensures its semi-regularity, modularity, fault tolerance, and algorithmic efficiency. In particular, the BSNs are special cases in which the two basis networks are the same. The Exchanged Hypercube is another example of GBSNs, i.e., EH(s,t) ≅ Gbsw(H(s), H(t)). The proposed network model is able to reveal the intrinsic relation between Swapped Networks and OTIS architectures. We are to prove the homomorphic relation between GBSNs and the Cartesian product of its two basis networks. We also show the key topological parameters of GBSNs that are related to the parameters of its basis networks. We have obtained the results on inter-node distances, a general simple routing algorithm, Halmitonian cycles for networks composed of Halmitonian basis networks with even number of nodes or same number of nodes. Finally, this paper provides a new layout style for hierarchical interconnection networks that offers the researcher an opportunity to explore the topological properties of networks more intuitively and insightfully.