  Research collaborations provide the foundation for scientific advances, but
we have only recently begun to understand how they form and grow on a global
scale. Here we analyze a model of the growth of research collaboration networks
to explain the empirical observations that the number of collaborations scales
superlinearly with institution size, though at different rates (heterogeneous
densification), the number of institutions grows as a power of the number of
researchers (Heaps' law) and institution sizes approximate Zipf's law. This
model has three mechanisms: (i) researchers are preferentially hired by large
institutions, (ii) new institutions trigger more potential institutions, and
(iii) researchers collaborate with friends-of-friends. We show agreement
between these assumptions and empirical data, through analysis of co-authorship
networks spanning two centuries. We then develop a theoretical understanding of
this model, which reveals emergent heterogeneous scaling such that the number
of collaborations between institutions scale with an institution's size.
