Hyperbolic embedding of multilayer networks.

Area of Science:

• Network Science
• Data Analysis
• Computational Biology

Background:

• Multilayer networks model complex systems with multiple connection types.
• Node embedding is crucial for analyzing these networks.
• Existing methods often embed layers independently, losing global structure.

Purpose of the Study:

• Introduce a novel hyperbolic embedding framework for multilayer networks.
• Enable layer-specific analysis while preserving global multilayer structure.
• Improve the analysis of complex systems with heterogeneous node sets and interlayer connections.

Main Methods:

• Developed a hyperbolic embedding framework supporting heterogeneous node sets.
• Generated layer-specific hyperbolic embeddings.
• Preserved global multilayer structure within hyperbolic space.

Main Results:

• Effectively preserved community structure in synthetic networks with varying node sets.
• Successfully clustered disease-related brain regions across different patients.
• Outperformed layer-independent approaches in real-world brain network analysis.

Conclusions:

• The proposed hyperbolic embedding is a robust tool for multilayer network analysis.
• Enhances interpretability and provides new insights into complex system structure and function.
• Relevant for comparative analysis in fields like neuroscience.