Scale-variant topological information for characterizing the structure of complex networks

Area of Science:

• Network Science
• Data Analysis
• Topology

Background:

• Real-world networks exhibit complex structures with varying scales and interactions, making them difficult to analyze.
• Traditional methods struggle to capture the dynamic and multifaceted nature of these networks.

Purpose of the Study:

• To develop a general framework for characterizing complex network structures.
• To address challenges posed by varying topological scales and nondyadic interactions.
• To provide insights into scale-variant topological information and network dynamics.

Main Methods:

• Utilizing topological data analysis (TDA) to map network nodes to point sets representing topological information at specific timescales.
• Analyzing the evolution of these point sets across variable timescales to capture scale-variant topological features.
• Employing a diffusion process at a single specified timescale for network node mapping.

Main Results:

• The proposed framework effectively identifies network models and classifies real-world networks.
• Demonstrated ability to detect transition points in time-evolving networks.
• Successfully applied to synthetic and real-world network data.

Conclusions:

• The TDA-based framework offers a unified approach for analyzing complex network structures.
• The method is applicable to intricate network types, including multilayer and multiplex networks.
• Provides a robust tool for understanding network topology and dynamics across scales.