Simulating urban scaling with a term linkages network of a university

In this paper, we make an attempt to increase our understanding of the urban scaling phenomenon. The aim is to 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 structure and simulate this structure by the network of all publications of a research intensive university. In this simulation, the publications take the role of the city inhabitants and the concepts (terms and keywords) in the publications represent all kinds of abilities and qualities of the inhabitants. We use in this experiment all author- and database-given terms of the scientific publications of Leiden University from 2022. 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. This procedure is performed for different values of the term occurrence threshold. We then analyze how four important network parameters, namely, number of terms, number of clusters, number of links, and total link strength increase with increasing size of the network. Particularly the number of network links and the total network linkage strength are in our opinion the parameters that dominate the scaling phenomenon and can be considered as a simulation of the socioeconomic strength of a city, that is, its gross urban product. We find a significant power law dependence of these network parameters on network size and the power law exponents for the lowest occurrence threshold are within the range that is typical for urban scaling. 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.