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

Area of Science:

• Computer Science
• Data Visualization
• Graph Theory

Background:

• Numerous graph layout techniques exist for diverse applications.
• Existing methods often lack a unified theoretical foundation, hindering comparison and development.
• Popular techniques include the spring-electrical model, stress model, and maxent-stress model.

Purpose of the Study:

• To present Taurus, a general framework unifying existing graph layout techniques.
• To enable systematic comparison of different layout methods and facilitate the development of new ones.
• To introduce a novel balanced stress model (BSM) for enhanced graph layout quality.

Main Methods:

• Developed a unified force representation based on quotient-based forces.
• Formulated existing techniques as combinations of power functions of graph-theoretical and Euclidean distances.
• Introduced a universal augmented stochastic gradient descent (SGD) optimizer for efficient solution finding.

Main Results:

• The Taurus framework successfully unifies popular graph layout techniques.
• The proposed balanced stress model (BSM) achieves superior graph layout quality.
• Comprehensive evaluations on synthetic and real graphs demonstrate the framework's effectiveness.
• An open-source package is released for easy comparison and customization of graph layout methods.

Conclusions:

• The Taurus framework provides a unified approach to graph layout, enabling better understanding and development.
• The balanced stress model (BSM) offers improved graph visualization quality.
• The open-source package empowers researchers and practitioners to utilize and extend these graph layout techniques.