  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.
