Universities Scale Like Cities

TL;DR

This paper demonstrates that universities exhibit urban-like nonlinear scaling in research output and impact, with deviations explained by local properties such as field composition and quality, paralleling city socioeconomic scaling.

Contribution

It reveals that university scaling behaviors mirror urban scaling laws and identifies local factors influencing deviations, advancing understanding of research productivity patterns.

Findings

Universities show power law scaling similar to cities in citations and publications.

Deviations from scaling laws are explained by local properties like field composition and impact.

Top universities' scaling exponents are comparable to urban scaling exponents.

Abstract

Recent studies of urban scaling show that important socioeconomic city characteristics such as wealth and innovation capacity exhibit a nonlinear, particularly a power law scaling with population size. These nonlinear effects are common to all cities, with similar power law exponents. These findings mean that the larger the city, the more disproportionally they are places of wealth and innovation. Local properties of cities cause a deviation from the expected behavior as predicted by the power law scaling. In this paper we demonstrate that universities show a similar behavior as cities in the distribution of the gross university income in terms of total number of citations over size in terms of total number of publications. Moreover, the power law exponents for university scaling are comparable to those for urban scaling. We find that deviations from the expected behavior can indeed be explained by specific local properties of universities, particularly the field-specific composition of a university, and its quality in terms of field-normalized citation impact. By studying both the set of the 500 largest universities worldwide and a specific subset of these 500 universities -- the top-100 European universities -- we are also able to distinguish between properties of universities with as well as without selection of one specific local property, the quality of a university in terms of its average field-normalized citation impact. It also reveals an interesting observation concerning the working of a crucial property in networked systems, preferential attachment.