Small-world behavior in time-varying graphs

TL;DR

This paper introduces the concept of temporal small-world networks, capturing the dynamic clustering and short average distances in time-varying graphs, with applications to synthetic and real-world systems.

Contribution

It defines temporal paths and distances, and characterizes small-world behavior in dynamic networks, extending static network analysis to time-varying systems.

Findings

Temporal small-world networks exhibit high temporal clustering and short average temporal distances.

Synthetic and real-world time-varying networks demonstrate small-world properties.

The framework captures dynamic connectivity patterns beyond static graph measures.

Abstract

Connections in complex networks are inherently fluctuating over time and exhibit more dimensionality than analysis based on standard static graph measures can capture. Here, we introduce the concepts of temporal paths and distance in time-varying graphs. We define as temporal small world a time-varying graph in which the links are highly clustered in time, yet the nodes are at small average temporal distances. We explore the small-world behavior in synthetic time-varying networks of mobile agents, and in real social and biological time-varying systems.