Efficient embedding of complex networks to hyperbolic space via their Laplacian

Area of Science:

• Network Science
• Data Science
• Computational Topology

Background:

• Complex network growth processes embed information in their topologies.
• Predicting structural network changes is a key research area.
• Existing hyperbolic embedding methods optimize for a specific network growth model.

Purpose of the Study:

• To introduce a novel, efficient, and data-driven manifold learning approach for complex network analysis.
• To enable quick geometric analysis of large-scale networks.
• To provide an alternative to existing network embedding techniques for network evolution and link prediction.

Main Methods:

• Laplacian-based Network Embedding (LNE) is proposed as a manifold learning technique.
• LNE utilizes geometric analysis for understanding network structure.
• The method is data-driven and efficient for large networks.

Main Results:

• LNE offers a simple, accurate, and efficient approach to network embedding.
• The method facilitates rapid geometric analysis of complex networks.
• Comparisons show LNE's applicability in network evolution and link prediction tasks.

Conclusions:

• Laplacian-based Network Embedding is a powerful tool for analyzing complex network growth and evolution.
• This approach provides an effective alternative for network link prediction.
• The method's efficiency and accuracy make it suitable for large-scale network analysis.