Structure Entropy, Self-Organization, and Power Laws in Urban Street Networks: Evidence for Alexander's Ideas

The study of networking mechanism is of central importance for better understanding the broader properties and phenomena of networks. Here, we investigate the scale-free networking in urban street networks holistically within the framework of information physics and statistical physics. Although the number of times that a natural road (a substitute for `namedu0027 street) crosses an other one has been widely reported to follow a scale-free probability distribution among self-organized cities, the derivation of the statistics of urban street networks from fundamental principles has focused very little attention. We recover the discrete Pareto probability distribution for natural roads in self-organized cities, and foresee a nonstandard bell-shaped probability distribution with a Paretian tail for their junctions. Our approach explicitly emphasizes the road-junction hierarchy rather than implicitly inhibiting it as in most investigations. This holistic viewpoint reveals an underlying Galoisean algebraic structure. So that our approach fits with the mindset of information physics. This enables us to envisage urban street networks as evolving social systems subject to a Boltzmann-mesoscopic entropy conservation. The passage from the underlying Galoisean hierarchy to an underlying Paretian coherence occurs by invoking Jaynesu0027s Maximum Entropy principle. Ultimately, to obtain the predicted statistics, we untangle the underlying discrete Pareto probability distribution with a binomial paired-agent social model taken at the asymptotic limit. The emerging paradigm may apply to systems with a more intricate hierarchy. Meanwhile, along your findings, it appears to reflect well Alexanderu0027s ideas on cities. The established statistics can be useful to build realistic urban models and to discover underlying laws that govern our cities.