Force-directed algorithm is one of the most commonly used methods for visualization of 2D graphs. These algorithms can be applied to a plethora of applications such as data visualization, social network analysis, crypto-currency transactions, and wireless sensor networks. Due to their effectiveness in visualization of topological data, various force-directed algorithms for 2D graphs were proposed in recent years. Although force-directed algorithms for 2D graphs were extensively investigated in research community, the algorithms for 3D graph visualization were rarely reported in the literature. In this paper, we propose four novel clustering-based force-directed (CFD) algorithms for visualization of 3D graphs. By using clustering algorithms, we divide a large graph into many smaller graphs so that they can be effectively processed by force-directed algorithms. In addition, weights are also introduced to further enhance the calculation for clusters. The proposed CFD algorithms are tested on 3 datasets with varying numbers of nodes. The experimental results show that proposed algorithms can significantly reduce edge crossings in visualization of large 3D graphs. The results also reveal that CFD algorithms can also reduce Kamada and Kawai energy and standardized variance of edge lengths in 3D graph visualization.

中文翻译：

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用于 3D 图形可视化的基于聚类的力导向算法

力导向算法是最常用的二维图形可视化方法之一。这些算法可应用于大量应用，例如数据可视化、社交网络分析、加密货币交易和无线传感器网络。由于它们在拓扑数据可视化方面的有效性，近年来提出了各种用于二维图的力导向算法。尽管研究界广泛研究了用于 2D 图的力导向算法，但文献中很少报道用于 3D 图可视化的算法。在本文中，我们提出了四种新颖的基于聚类的力导向 (CFD) 算法，用于 3D 图的可视化。通过使用聚类算法，我们将一个大图划分为许多较小的图，以便力导向算法可以有效地处理它们。此外，还引入了权重以进一步增强对集群的计算。建议的 CFD 算法在具有不同节点数量的 3 个数据集上进行了测试。实验结果表明，所提出的算法可以显着减少大型 3D 图形可视化中的边缘交叉。结果还表明，CFD 算法还可以减少 Kamada 和 Kawai 能量以及 3D 图形可视化中边长的标准化方差。实验结果表明，所提出的算法可以显着减少大型 3D 图形可视化中的边缘交叉。结果还表明，CFD 算法还可以减少 Kamada 和 Kawai 能量以及 3D 图形可视化中边长的标准化方差。实验结果表明，所提出的算法可以显着减少大型 3D 图形可视化中的边缘交叉。结果还表明，CFD 算法还可以减少 Kamada 和 Kawai 能量以及 3D 图形可视化中边长的标准化方差。