Systematic comparison of graph embedding methods in practical tasks.

Area of Science:

• Graph theory and network analysis
• Machine learning and data representation

Background:

• Network embedding represents graph structures in geometric spaces for downstream tasks like link prediction and clustering.
• A wide array of graph embedding methods necessitates guidance for practitioners to select appropriate approaches for specific applications.

Purpose of the Study:

• To systematically compare 11 diverse network embedding methods.
• To evaluate embedding performance across Euclidean, hyperbolic, and community-based spaces.
• To provide a standardized benchmark for network embedding evaluation.

Main Methods:

• Applied 11 network embedding techniques to over 100 real-world and synthetic networks.
• Evaluated embedding quality using mapping accuracy, greedy routing, and link prediction tasks.
• Compared running times and analyzed the impact of network characteristics (e.g., degree distribution, modularity).

Main Results:

• Euclidean embedding methods demonstrated superior performance in greedy routing tasks.
• Hyperbolic and community-based embedding methods outperformed Euclidean approaches in link prediction.
• Performance varied based on network characteristics, influencing embedding quality.

Conclusions:

• The choice of network embedding method significantly impacts downstream task performance.
• Hyperbolic and community-based methods offer advantages for link prediction.
• A standardized evaluation framework is provided to aid method selection and development.