Optimizing Network Topology Efficiency: A Resource-Centric Analysis of Non-Blocking Architectures

In modern network design, "efficiency" is often conflated with raw performance metrics like latency or aggregate throughput. This paper proposes a resource-centric definition of efficiency, isolating the hardware cost required to maintain a non-blocking throughput constraint. By modeling network cost as a function of the Traffic Multiplier (Hop Count) and Router Complexity (Radix), we demonstrate that the optimal topology is determined by the technological ratio between link interface costs ($α$), crossbar switching costs ($β$), and the network concentration ratio. We conclude that while high-radix direct networks optimize efficiency at small to medium scales, indirect networks (e.g., Fat Trees) are required to cap router complexity at massive scales. Furthermore, we posit that redundancy is most efficiently handled via parallel network instances (e.g., multi-plane Star networks) rather than intrinsic topological path diversity.