A dynamic model of time-dependent complex networks

TL;DR

This paper introduces a dynamic preferential attachment model to explain the rapid and irregular evolution of node centrality in large, fast-changing complex networks, challenging traditional static network assumptions.

Contribution

It proposes a novel dynamic model that captures the transient nature of node importance in evolving networks, differing from existing static or slowly changing network theories.

Findings

The model reproduces observed dynamic centrality phenomena.

It demonstrates a transition from random walk to preferential attachment.

The approach explains the lack of continuity in node importance over time.

Abstract

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness against failures, vulnerability to deliberate attacks, and diffusion properties. However, recent empirical research of large dynamic networks (characterized by connections that are irregular and evolve rapidly) has demonstrated that there is little continuity in degree centrality of nodes over time, even when their degree distributions follow a power law. This unexpected dynamic centrality suggests that the connections in these systems are not driven by preferential attachment or other known mechanisms. We present a novel approach to explain real-world dynamic networks and qualitatively reproduce these dynamic centrality phenomena. This approach is based on a dynamic preferential attachment mechanism, which exhibits a sharp transition from a base pure random walk scheme.