Transforming Network Topology Design from Art to Science For decades, the design of large-scale network topologies has relied heavily on heuristic intuition and bottom-up engineering experience. While classic structures like Fat-tree have achieved immense success, the underlying mathematical principles governing their performance have remained largely implicit. This book introduces the first general framework capable of systematically generating and optimizing large-scale network topologies through a rigorous top-down approach. It reveals the hidden mathematical principles behind successful engineering designs, using Ramanujan graphs and combinatorial designs to achieve the optimal trade-off among various performance metrics. From clarifying the success of classic Fat-tree topology to designing future-proof AI clusters, this framework provides a universal blueprint for next-generation interconnection networks. It is an essential guide for researchers, engineers, industry professionals and students seeking to master the topology design and analysis of interconnection networks. Topics explored in this book include: • Mathematical background of topology design, including basic graph theory, algebra graph theory and combinatorial design • A unified topology design flow, including intra-module design, connection design, inter-module design, and finalization • Reinterpretation and evolution of several representative topology design instances, including families of fat-tree, HyperX, Dcell, and Bcube • The design method of brand-new topologies from scratch and guiding principles for the selection of design patterns and parameters • Applications to intelligent computing center (AI Cluster) and other emerging scenarios • Future directions of topology design, including both theoretical exploration and practical extension
