title: Superlinear and sublinear urban scaling in geographical networks modeling cities.
abstract: Using a geographical scale-free network to describe relations between people in a city, we explain both superlinear and sublinear allometric scaling of urban indicators that quantify activities or performances of the city. The urban indicator Y(N) of a city with the population size N is analytically calculated by summing up all individual activities produced by person-to-person relationships. Our results show that the urban indicator scales superlinearly with the population, namely, Y(N)∝N(β) with β>1, if Y(N) represents a creative productivity and the indicator scales sublinearly (β<1) if Y(N) is related to the degree of infrastructure development. These results coincide with allometric scaling observed in real-world urban indicators. We also show how the scaling exponent β depends on the strength of the geographical constraint in the network formation.
authors.affiliation: Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan.
authors.forename: K
authors.initials: K
authors.lastname: Yakubo
authors.forename: Y
authors.initials: Y
authors.lastname: Saijo
authors.affiliation: University of Maribor, Slomškov trg 15, Maribor SI-2000, Slovenia.
authors.forename: D
authors.initials: D
authors.lastname: Korošak
mesh_terms: D002947:Cities; D003198:Computer Simulation; D005843:Geography; D006801:Humans; D007398:Interpersonal Relations; D016014:Linear Models; D014505:Urban Population