Systematic comparison of graph embedding methods in practical tasks

TL;DR

This paper systematically compares eleven graph embedding methods across various real-world and synthetic networks, evaluating their effectiveness in tasks like link prediction, routing, and clustering to guide practitioners in method selection.

Contribution

It provides a comprehensive benchmark and analysis of multiple embedding techniques in different spaces, highlighting their strengths and weaknesses for practical applications.

Findings

Euclidean methods excel in greedy routing

Community-based and hyperbolic methods outperform in link prediction

Embedding performance varies with network characteristics

Abstract

Network embedding techniques aim at representing structural properties of graphs in geometric space. Those representations are considered useful in downstream tasks such as link prediction and clustering. However, the number of graph embedding methods available on the market is large, and practitioners face the non-trivial choice of selecting the proper approach for a given application. The present work attempts to close this gap of knowledge through a systematic comparison of eleven different methods for graph embedding. We consider methods for embedding networks in the hyperbolic and Euclidean metric spaces, as well as non-metric community-based embedding methods. We apply these methods to embed more than one hundred real-world and synthetic networks. Three common downstream tasks -- mapping accuracy, greedy routing, and link prediction -- are considered to evaluate the quality of the various embedding methods. Our results show that some Euclidean embedding methods excel in greedy routing. As for link prediction, community-based and hyperbolic embedding methods yield overall performance superior than that of Euclidean-space-based approaches. We compare the running time for different methods and further analyze the impact of different network characteristics such as degree distribution, modularity, and clustering coefficients on the quality of the different embedding methods. We release our evaluation framework to provide a standardized benchmark for arbitrary embedding methods.