Environmental Influences on Collaboration Network Evolution: A Historical Analysis

TL;DR

This study analyzes long-running collaboration networks to quantify how major historical events affect network growth and collaboration patterns. By modeling MAG (1800-2020) and IMDb (1900-2020) as temporal undirected graphs and applying a fixed project duration to infer initiation times, the authors compare node and edge dynamics across epochs such as La Belle Epoque and the World Wars. Key findings show lasting impacts on node recruitment (e.g., declines of $45\%$–$52\%$ in MAG during wars) while edge formation preserves power-law structure with $\gamma$-values of $1.6 \pm 0.1$ (MAG) and $2.1 \pm 0.1$ (IMDb), and Weibull-distributed collaboration durations with $k$-parameters $0.2 \pm 0.02$ (MAG) and $0.5 \pm 0.03$ (IMDb). The paper also identifies a robust timescale coupling with $\tau_N/\tau_E \approx 2$–$3$ that persists through disruptions and shows domain-specific recovery trajectories, including a rapid post-war acceleration in academia and slower yet steadier recovery in entertainment. These results advance network theory by demonstrating environment-driven, long-term coupling between growth and collaboration, with practical implications for designing resilient, enduring collaborative systems under external disruption.

Abstract

We analysed two large collaboration networks -- the Microsoft Academic Graph (1800-2020) and Internet Movie Database (1900-2020) -- to quantify network responses to major historical events. Our analysis revealed four properties of network-environment interaction. First, historical events can influence network evolution, with effects persisting far longer than previously recognised; the academic network showed 45\% declines during World Wars and 90\% growth during La Belle Epoque. Second, node and edge processes exhibited different environmental sensitivities; while node addition/removal tracked historical events, edge formation maintained stable statistical properties even during major disruptions. Third, different collaboration networks showed distinct response patterns; academic networks displayed sharp disruptions and rapid recoveries, while entertainment networks showed gradual changes and greater resilience. Fourth, both networks developed increasing resilience. Our results provide new insights for modelling network evolution and managing collaborative systems during periods of external disruption.

Figures (8)

• Figure 1: Evolution of node counts in the MAG (top) and IMDb (bottom) networks on logarithmic scales. Left panels show absolute counts: cumulative total nodes (black line), nodes active with new edges that year (red line), and new nodes joining that year (green line). Right panels show the same data normalised by contemporary world population. Grey bands show major historical events: La Belle Epoque (1890-1914), World War I (1914-1918), and World War II (1939-1945). Population data post-1950 uses official UN records; earlier values are linearly interpolated between historical estimates. Note the distinct change in MAG growth rate around 1950 and the different sensitivities to historical events between networks.
• Figure 2: Characteristic timescales of network processes, shown on logarithmic scales. Top panels: MAG network timescales; Bottom panels: IMDb network timescales. Left panels show node timescales: addition (black) and removal (red). Right panels show edge timescales: addition (black) and removal (red). Timescales are computed as the ratio of total quantity to its rate of change. Note the parallel evolution of timescales within each network despite their different absolute values, and the stability of their ratios over centuries of evolution.
• Figure 3: The fraction of new participants per year in the MAG (left) and IMDb (right) networks, showing the balance between new entrants and established participants. The academic network shows a gradual decrease in the fraction of new authors, while the entertainment network maintains a more stable ratio.
• Figure 4: Parameter evolution of the power law fits to the edge-addition probability distributions in the MAG and IMDb networks.
• Figure 5: Evolution of collaboration event counts in the networks. Top row shows MAG network: absolute count of papers (left) and relative fractions by author count (right). Bottom row shows IMDb network: absolute count of movies (left) and relative fractions by lead actor count (right). Both networks show systematic changes in the distribution of collaboration size.