N.V. Blokhin1

1 Financial University under the Government of the Russian Federation (Moscow, Russia)

1nvblokhin@fa.ru

Visualization plays a crucial role in network structure analysis, enabling researchers to effectively identify structural features, patterns, and relationships in a network. In many cases, it is necessary to focus on a specific node and its neighborhood to examine the local graph structure in detail. One way to achieve this is to incorporate a hierarchical structure into the layout, which enhances clarity and improves the perception of network organization. However, traditional layout algorithms are often unsuitable for such visualizations, as they are either not designed to support hierarchical structures or are limited to tree-like graphs. Additionally, real-world networks often contain meaningful node and edge attributes that classical algorithms tend to overlook, potentially reducing the quality and interpretability of the resulting visualizations. To address these limitations, this study proposes a novel approach that integrates a modern machine learning model, namely graph neural networks, with classical force-directed methods. The core idea of the developed algorithm is to preserve the advantages of force-based layouts, such as natural and balanced node distribution, but also to extend the layout with a hierarchical component to enhance readability. By introducing a concentric force mechanism, the method enhances the intuitive representation of node neighborhoods, facilitating the analysis of local structures in complex networks. Additionally, it integrates node attributes into the layout, adding depth to the visualization and improving its overall clarity and expressiveness.

The proposed method was evaluated on both synthetic graphs, such as trees, and real-world company relationship graphs, which do not have a tree structure but are still effectively handled by the algorithm. The results confirm that the algorithm effectively distributes nodes in a way that preserves the fundamental properties of classical methods while introducing a layered, orbital arrangement that improves clarity. Additionally, the analysis highlights the impact of node attributes on the final layout, showing that their inclusion enhances both the accuracy and interpretability of the visualization. Developed hybrid approach has significant practical applications, particularly in network analysis tasks where both global structure and local details are important. By combining the strengths of force-directed methods with hierarchical structuring and attribute awareness, the proposed algorithm provides a flexible and powerful tool for graph visualization, offering improved usability in applied research and practical data analysis scenarios.

Blokhin N.V. Method for constructing hierarchical graph layout based on spring algorithms and graph neural networks. Information-measuring and Control Systems. 2025. V. 23. № 3. P. 37−46. DOI: https://doi.org/10.18127/j20700814-202503-04 (in Russian)

1. Ylinen H. Improvements to a Force-Directed Method for Graph Drawing: выпускная квалификационная работа магистра. Хельсинки. 2003. 91 с.
2. Zachary W. An information flow model for conflict and fission in small groups // Journal of Anthropological Research. 1977. № 33. С. 452−473.
3. Kobourov S. Spring embedders and force directed graph drawing algorithms. Preprint arXiv:1201.3011. 2012.
4. Eades P. A heuristic for graph drawing // Congressus numerantium. 1984. № 42. С. 149−160.
5. Fruchterman T., Reingold E. Graph drawing by force-directed placement // Software: Practice and Experience. 1991. № 11. С. 1129−1164.
6. Kamada T., Kawai S. An algorithm for drawing general undirected graphs // Inform. Process. Lett. 1989. № 31. С. 7−15.
7. Herman I., Melancon G., Marshall M. Graph visualization and navigation in information visualization: A survey // IEEE Transactions on Visualization and Computer Graphics. 2000. № 1. С. 24−43.
8. Both C., Dehmamy N., Yu R., Barabási A. Accelerating network layouts using graph neural networks // Nature Communications. 2023. Т. 14.
9. Huang W., Luo J., Bednarz T., Duh H. Making Graph Visualization a User-Centered Process // Journal of Visual Languages & Computing. 2018. Т. 48.
10. Bennett C., Ryall J., Spalteholz L., Gooch A. The Aesthetics of Graph Visualization // Proceedings of Computational Aesthetics in Graphics. Visualization and Imaging. 2007. С. 57−64.
11. Gilmer J., Schoenholz S., Riley P., Vinyals O., Dahl G. Message passing neural networks // Machine Learning Meets Quantum Physics. 2020. С. 199−214.
12. Kipf T., Welling M. Semi-Supervised Classification with Graph Convolutional Networks. ArXiv abs/1609.02907. 2016.
13. PyG Documentation. URL: https://pytorch-geometric.readthedocs.io/ (дата обращения: 25.01.2025).
14. NetworkX documentation. URL: https://networkx.org/ (дата обращения: 25.01.2025).
15. Lamping J., Rao R. The Hyperbolic Browser: A Focus + Context Technique for Visualizing Large Hierarchies // J. Vis. Lang. Comput. 1996. Т. 7. С. 33−55.