Universities Scale Like Cities

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.

💡 Research Summary

The paper “Universities Scale Like Cities” investigates whether the well‑known scaling laws that link city population to socioeconomic output also apply to higher‑education institutions. Urban scaling research has repeatedly shown that many city‑level indicators (gross domestic product, innovation, crime, etc.) follow a power‑law relationship of the form Y = Y₀·X^β, where X is population, Y is the indicator, and the exponent β is typically greater than one. A β > 1 implies super‑linear scaling: larger cities generate disproportionately more wealth or innovation per capita.

The authors transpose this framework to universities by defining the “size” of a university as the total number of publications (P) it produces and its “gross income” as the total number of citations (C) those publications receive. Citations are treated as a proxy for academic wealth because they reflect both the visibility and impact of research output. The central hypothesis is that C scales with P according to a power law C = C₀·P^β, with β comparable to urban values.

To test the hypothesis, the authors assembled two datasets. The first comprises the 500 largest research universities worldwide, identified through the total number of indexed publications between 2015 and 2020 in Scopus and Web of Science. The second is a focused subset of the top‑100 European universities drawn from the same global list. For each institution they extracted (i) the total publication count, (ii) the total citation count, (iii) the field‑normalized citation impact (NCI), and (iv) the disciplinary composition (the share of publications in STEM versus humanities/social sciences).

Using ordinary least‑squares regression on log‑transformed data (log C = α + β log P), the authors find β ≈ 1.15 for the global 500‑university sample and β ≈ 1.12 for the European 100‑university sample. Both exponents lie squarely within the range reported for urban scaling (≈ 1.10–1.20). This result demonstrates that, like cities, universities exhibit super‑linear scaling: doubling the number of papers yields more than double the citations.

However, individual universities deviate from the average scaling line. To explain these residuals, the authors introduce two “local” variables. First, the disciplinary mix: institutions with a higher proportion of STEM publications tend to sit above the scaling line because STEM fields generally attract more citations, while those dominated by humanities and social sciences fall below. Second, the average field‑normalized citation impact (NCI), which adjusts raw citations for field‑specific citation practices. Universities with high NCI consistently show positive residuals, indicating that research quality, not just quantity, drives excess citation accumulation. A multivariate regression shows that disciplinary composition accounts for roughly 35 % of the variance in residuals, NCI for about 28 %, and together they explain over 60 % of the deviations.

The paper further links these findings to the concept of preferential attachment—a mechanism well‑studied in network science where nodes that already have many connections are more likely to acquire new ones. In the university context, larger institutions that already enjoy high citation counts attract top scholars, larger research grants, and more collaborative opportunities, which in turn generate additional citations. This feedback loop mirrors the way megacities draw disproportionate economic activity, reinforcing the analogy between urban and academic systems.

A comparative analysis of the two samples reveals that the European elite universities have, on average, a 30 % higher NCI and a 15 percentage‑point greater STEM share than the global 500‑university set. Despite these quality advantages, the scaling exponent β does not differ dramatically, suggesting that the underlying super‑linear mechanism is robust to variations in research excellence. What does change is the dispersion of residuals: the elite sample shows a tighter distribution, implying that high‑quality institutions conform more closely to the expected scaling law.

In conclusion, the study provides strong empirical evidence that universities obey the same super‑linear scaling laws observed in cities. The magnitude of the exponent indicates that size confers a disproportionate advantage in generating scholarly impact, but this advantage is modulated by local factors such as disciplinary focus and normalized citation impact. For policymakers and university administrators, the findings imply that strategies aimed solely at increasing publication volume may yield diminishing returns unless accompanied by efforts to improve research quality and to diversify disciplinary portfolios. Moreover, recognizing the preferential‑attachment dynamics suggests that interventions designed to redistribute resources (e.g., targeted funding for smaller or under‑cited institutions) could help mitigate the concentration of academic wealth and promote a more balanced innovation ecosystem.