Low-Complexity Hyperbolic Embedding Schemes for Temporal Complex Networks.

Area of Science:

• Complex network analysis
• Graph embedding
• Hyperbolic geometry

Background:

• Hyperbolic embeddings effectively capture complex network properties.
• Existing methods struggle with the dynamic evolution of temporal complex networks.
• Adaptability and efficient updates for varying network scales remain challenges.

Purpose of the Study:

• To propose novel hyperbolic embedding schemes for temporal complex networks.
• To address challenges in adaptability and embedding updates for dynamic networks.
• To develop efficient methods for both medium and large-scale networks.

Main Methods:

• A low-complexity hyperbolic embedding scheme using matrix perturbation for medium-scale networks.
• Geometric initialization by merging nodes in a hyperbolic circular domain.
• R-tree based search for fast initialization in large-scale networks.

Main Results:

• Proposed schemes demonstrate low computational complexity.
• Methods are adaptable to networks of varying scales and dynamic changes.
• Effective performance across synthetic and realistic temporal networks in downstream tasks.

Conclusions:

• The developed hyperbolic embedding schemes are efficient and scalable.
• These methods offer robust solutions for analyzing temporal complex networks.
• The approach enhances understanding of dynamic network structures and their evolution.