Simulating Urban Scaling with an Term Linkages Network of a University

Abstract

In this paper we make an attempt to increase our understanding of the urban scaling phenomenon. We investigate how superlinear scaling emerges if a network increases in size and how this scaling depends on the occurrence of elements that constitute the network. To this end we consider a city as a complex network and simulate this by the network of publications of a university. In this simulation the publications take the role of the city inhabitants and the concepts (terms) in the publications represent abilities and qualities of the inhabitants. We calculate the co-occurrence of terms, and on the basis of these connections we create a network and let this network grow by successively adding publications from the total set of publications. In this way we get a series of networks with different sizes and this simulates a series of cities with different number of inhabitants. We analyze how four network parameters increase with increasing size of the network. The number of network links and the total network linkage strength are the parameters that dominate the scaling phenomenon and can be considered as a simulation of the socioeconomic strength of a city. We find a significant power law dependence of these network parameters on network size. In our approach the number of clusters can be interpreted as a measure of complexity within the network. Since the occurrence threshold determines the diversity of terms, we may expect a special relation between the occurrence threshold and the number of clusters. This is indeed the case: whereas for the three other network parameters the scaling exponent increases with increasing occurrence threshold, the number of clusters is the only network parameter of which the scaling exponent decreases with increasing occurrence threshold. Finally, we discuss how our publication term network approach relates to scaling phenomena in cities.