Explosive Growth in Large-Scale Collaboration Networks

Abstract

We analyse the evolution of two large collaboration networks: the Microsoft Academic Graph (1800-2020) and Internet Movie Database (1900-2020), comprising $2.72\times 10^8$ and $1.88\times 10^6$ nodes respectively. The networks show super-linear growth, with node counts following power laws $N(t)\propto t^{\hat{I}}\pm$ where $\hat{I}\pm =2.3$ increasing to $3.1$ after 1950 (MAG) and $\hat{I}\pm =1.8$ (IMDb). Node and edge processes maintain stable but noisy timescale ratios ($\ddot{I}{„}_N/\ddot{I}{„}_E\approx 2.8\pm 0.3$ MAG, $2.3\pm 0.2$ IMDb). The probability of waiting a time $t$ between successive collaborations was found to be scale-free, $P(t)\propto t^{-{\hat{I}}^3}$, with indices evolving from ${\hat{I}}^3\approx 2.3$ to $1.6$ (MAG) and $2.6$ to $2.1$ (IMDb). Academic collaboration sizes increased from $1.2$ to $5.8$ authors per paper, while entertainment collaborations remained more stable ($3.2$ to $4.5$ actors). These observations indicate that current network models might be enhanced by considering accelerating growth, coupled timescales, and environmental influence, while explaining stable local properties.