Parametric Analysis of Network Evolution Processes

TL;DR

This study addresses how node (career) and edge (collaboration) lifetimes evolve in two large-scale collaboration networks, the MAG and IMDb. It adopts a cohort-based empirical approach and Weibull modelling to quantify lifetime distributions, revealing universal Weibull shapes with $k \approx 0.2$ for academic careers and $k \approx 0.5$ for entertainment careers, persisting across centuries. While career longevity shows universal patterns, collaboration dynamics diverge: academic collaborations lengthen over time with increasing $\lambda$, whereas entertainment collaborations remain relatively stable, maintaining heavy-tailed lifetimes. These findings constrain social network evolution models to incorporate universal lifetime distributions alongside domain-specific growth dynamics, with implications for policy design and institutional strategies to foster durable collaboration patterns.

Abstract

We present a comprehensive parametric analysis of node and edge lifetimes processes in two large-scale collaboration networks: the Microsoft Academic Graph (1800-2020) and Internet Movie Database (1900-2020). Node and edge lifetimes (career and collaboration durations) follow Weibull distributions with consistent shape parameters ($k \approx 0.2$ for academic, $k \approx 0.5$ for entertainment careers) across centuries of evolution. These distributions persist despite dramatic changes in network size and structure. Edge processes show domain-specific evolution: academic collaboration durations increase over time (power-law index $1.6$ to $2.3$) while entertainment collaborations maintain more stable patterns (index $2.6$ to $2.1$). These findings indicate that while career longevity exhibits consistent patterns, collaboration dynamics appear to be influenced by domain-specific factors. The results provide new constraints for models of social network evolution, requiring incorporation of both universal lifetime distributions and domain-specific growth dynamics.

Figures (22)

• Figure 1: $\chi^{2}$ and fitting parameter evolution for the career duration distributions shown in Figs. \ref{['mag_careers_a']} to \ref{['imdb_careers_c']}.
• Figure 2: $\chi^{2}$ and fitting parameter evolution for the collaboration duration distributions shown in Figs. \ref{['mag_edges_removal_a']}-\ref{['imdb_edges_removal_c']}.
• Figure 3: Distributions of the number of authors with a given career duration, for cohorts of authors who first published in a given year, 1800 to 1824. A power-law fit, Weibull fit, and a Weibull fit excluding the central data point are shown in black, green, and blue lines respectively. Note that the y-axis scale is the same in all plots.
• Figure 4: Distributions of the number of authors with a given career duration, for cohorts of authors who first published in a given year, 1825 to 1859. A power-law fit, Weibull fit, and a Weibull fit excluding the central data point are shown in black, green, and blue lines respectively. Note that the y-axis scale is the same in all plots.
• Figure 5: Distributions of the number of authors with a given career duration, for cohorts of authors who first published in a given year, 1850 to 1874. A power-law fit, Weibull fit, and a Weibull fit excluding the central data point are shown in black, green, and blue lines respectively. Note that the y-axis scale is the same in all plots.