Parametric Analysis of Network Evolution Processes

TL;DR

This paper analyzes the lifetimes of nodes and edges in large-scale collaboration networks, revealing consistent distribution patterns over centuries and domain-specific evolution in collaboration durations, informing social network models.

Contribution

It provides the first comprehensive parametric analysis of node and edge lifetimes across two major large-scale networks over extensive historical periods.

Findings

Node and edge lifetimes follow Weibull distributions with consistent shape parameters.

Academic collaboration durations increase over time, while entertainment collaborations remain stable.

Universal lifetime distributions coexist with domain-specific collaboration dynamics.

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.