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Easy and intuitive navigability is of central importance in cities. Theactual scale-free networking of urban street networks in their topologicalspace, where navigation information is encoded by mapping roads to nodes andjunctions to links between nodes, has still no simple explanation. Emphasizingthe road-junction hierarchy in a holistic and systematic way leads us toenvisage urban street networks as evolving social systems subject to aBoltzmann-mesoscopic entropy conservation. This conservation, which we mayinterpret in terms of surprisal, ensures the passage from the road-junctionhierarchy to a scale-free coherence. To wit, we recover the actual scale-freeprobability distribution for natural roads in self-organized cities. We obtainthis passage by invoking Jaynes's Maximum Entropy principle (statisticalphysics), while we capitalize on modern ideas of quantification (informationphysics) and well known results on structuration (lattice theory) to measurethe information network entropy. The emerging paradigm, which applies tosystems with more intricate hierarchies as actual cities, appears to reflectwell the influential ideas on cities of the urbanist Christopher Alexander.

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