Topological clustering of multilayer networks

Area of Science:

• Complex Systems Science
• Network Science
• Topological Data Analysis

Background:

• Multilayer networks model interdependent systems like infrastructure and brain connectomes.
• Clustering these networks, especially using higher-order interactions, is underdeveloped.
• Higher-order connectivity is crucial for applications like infrastructure security and medical diagnosis.

Purpose of the Study:

• To introduce a topological approach for clustering multilayer networks.
• To group nodes based on the shape similarity of their local neighborhoods.
• To address limitations in current clustering methods for complex, interdependent systems.

Main Methods:

• Applying topological data analysis concepts to multilayer networks.
• Developing a novel clustering method named clustering using persistence diagrams (CPD).
• Quantifying local neighborhood shapes using topological summaries (persistence diagrams).

Main Results:

• CPD systematically captures heterogeneous higher-order interaction properties within and between network layers.
• The method integrates information from node neighbors for robust clustering.
• Demonstrated utility in vulnerability zoning for weather- and climate-induced risks in property insurance.

Conclusions:

• Clustering using persistence diagrams (CPD) offers a powerful new method for analyzing multilayer networks.
• CPD effectively leverages higher-order interactions and topological features for node grouping.
• The approach has significant potential for applications in critical infrastructure, neuroscience, and risk assessment.