Kinematic-Based Force-Directed Graph Embedding

Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis tasks like node classification, link prediction, and visualization. In this paper, we propose and provide proof of convergence for a novel graph embedding paradigm where nodes are assumed to possess mass and a kinematic-based force-directed model is applied to calculate embedding gradients. Our proposed force-directed graph embedding method utilizes the steady acceleration kinematic equations to embed nodes in a way that preserves graph topology and structural features. This method simulates a set of customized attractive and repulsive forces between all node pairs with respect to their hop distance. These forces are then used in Newton’s second law to obtain the acceleration of each node. The method is intuitive, parallelizable, and highly scalable. We evaluate our method on several graph analysis tasks and show that it achieves competitive performance compared to state-of-the-art unsupervised embedding techniques.