Explosive Growth in Large-Scale Collaboration Networks

TL;DR

This study analyzes the explosive, super-linear growth of large-scale collaboration networks like Microsoft Academic Graph and IMDb, revealing evolving power-law dynamics, stable timescale ratios, and scale-free collaboration waiting times over two centuries.

Contribution

It provides a comprehensive analysis of the growth patterns and temporal dynamics of large collaboration networks, highlighting the need for improved models considering accelerating growth and environmental factors.

Findings

Networks exhibit super-linear growth with power-law node increase.

Waiting times between collaborations follow a scale-free distribution.

Collaboration sizes vary over time, with academic collaborations increasing more than entertainment.

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 $N(t) \propto t^{\alpha}$ where $\alpha = 2.3$ increasing to $3.1$ after 1950 (MAG) and $\alpha = 1.8$ (IMDb). Node and edge processes maintain stable but noisy timescale ratios ($\tau_N/\tau_E \approx 2.8 \pm 0.3$ MAG, $2.3 \pm 0.2$ IMDb). The probability of waiting a time $t$ between successive collaborations was found to be scale-free, $P(t) \propto t^{-\gamma}$, with indices evolving from $\gamma \approx 2.3$ 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.