Taurus: Towards a Unified Force Representation and Universal Solver for Graph Layout

• Published in: IEEE transactions on visualization and computer graphics Vol. 29; no. 1; pp. 1 - 10
• Main Authors: Xue, Mingliang, Wang, Zhi, Zhong, Fahai, Wang, Yong, Xu, Mingliang, Deussen, Oliver, Wang, Yunhai
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Computational modeling; Force; Framework; Gradient Descent; Graph drawing; Graph Layout; Graphs; Layout; Layouts; Representations; Springs; Stress
• ISSN: 1077-2626; 1941-0506; 1941-0506
• DOI: 10.1109/TVCG.2022.3209371

Over the past few decades, a large number of graph layout techniques have been proposed for visualizing graphs from various domains. In this paper, we present a general framework, Taurus, for unifying popular techniques such as the spring-electrical model, stress model, and maxent-stress model. It is based on a unified force representation, which formulates most existing techniques as a combination of quotient-based forces that combine power functions of graph-theoretical and Euclidean distances. This representation enables us to compare the strengths and weaknesses of existing techniques, while facilitating the development of new methods. Based on this, we propose a new balanced stress model (BSM) that is able to layout graphs in superior quality. In addition, we introduce a universal augmented stochastic gradient descent (SGD) optimizer that efficiently finds proper solutions for all layout techniques. To demonstrate the power of our framework, we conduct a comprehensive evaluation of existing techniques on a large number of synthetic and real graphs. We release an open-source package, which facilitates easy comparison of different graph layout methods for any graph input as well as effectively creating customized graph layout techniques.