A Transformative Topological Representation for Link Modeling, Prediction and Cross-Domain Network Analysis.

Area of Science:

• Network Science
• Data Mining
• Computational Topology

Background:

• Complex systems (social, biological, physical) are often represented as networks.
• Accurate link prediction is vital for understanding network structure and dynamics.
• Current methods struggle with dynamic link formation patterns, especially in cross-domain analyses.

Purpose of the Study:

• To propose a new, efficient, and interpretable link representation scheme.
• To enable accurate link prediction and topological feature engineering.
• To facilitate the study and comparison of link patterns across diverse networks.

Main Methods:

• Projecting the local network environment of a link onto a "dipole plane".
• Representing link topology as a differentiable point-cloud distribution.
• Developing a universal platform for profiling and comparing link patterns.

Main Results:

• Achieved comparable or superior results to state-of-the-art Graph Neural Networks (GNNs).
• Models are significantly smaller (up to hundreds of times) and run much faster.
• Identified common link formation patterns: bridge-style, radiation-style, and community-style.

Conclusions:

• The dipole plane representation offers expressiveness, interpretability, and generalization.
• This method provides a powerful tool for network analysis and cross-domain studies.
• Uncovered universal link formation principles applicable to various network types.