Scaling Laws of Self-organized Communication Networks: Transport Complexity

This chapter addresses the theoretical unification of network value scaling laws, aiming to resolve the disparities between Metcalfe’s Law and conflicting variants such as Sarnoff’s and Odlyzko’s laws. The study is pivotal as it seeks to provide a singular theoretical mechanism to explain these seemingly contradictory, yet empirically supported, scaling behaviors. Operating on the premise that “traffic represents value,” we establish a comprehensive network model that integrates geography, node influence, and relationship separation. The chapter structure systematically formulates the definition of traffic load, followed by the rigorous derivation of general analytical boundaries. Ultimately, the text elucidates the underlying mechanisms driving these laws, demonstrating how the proposed framework can reproduce various scaling behaviors—ranging from linear (n) to cubic ( \(n^3\) )—and validating these theoretical insights through empirical evaluation.