A Model of Densifying Collaboration Networks

TL;DR

This paper presents a model explaining how research collaboration networks grow and densify, capturing empirical patterns like superlinear scaling, Heaps' law, and Zipf's law through mechanisms such as preferential attachment and local collaboration.

Contribution

It introduces a novel model with three mechanisms that accurately reproduces empirical scaling laws and heterogeneity in research collaboration networks.

Findings

Model aligns with two-century co-authorship data

Reveals emergent heterogeneous scaling laws

Explains superlinear growth and densification patterns

Abstract

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.