The relationship between the topology of interconnection networks and their functional properties is examined. Graph-theoretical characterizations are derived for delta networks, which have a simple routing scheme, and for bidelta networks, which have the delta property in both directions. Delta networks are shown to have a recursive structure. Bidelta networks are shown to have a unique topology. The definition of bidelta network is used to derive in a uniform manner the labelling schemes that define the omega networks, indirect binary cube networks, flip networks, baseline networks, modified data manipulators and two new networks; these schemes are generalized to arbitrary radices. The labelling schemes are used to characterize networks with simple routing. In another paper (Kruskal/Snir, 1984), we characterize the networks with optimal performance/cost ratio. Only the multistage shuffle-exchange networks have both optimal performance/cost ratio and simple routing. This helps explain why few fundamentally different geometries have been proposed. © 1986.
Kruskal, C. P., & Snir, M. (1986). A unified theory of interconnection network structure. Theoretical Computer Science, 48(C), 75–94. https://doi.org/10.1016/0304-3975(86)90084-8