Topological Spatial Graph Reduction
Published:Dec 30, 2025 16:27
•1 min read
•ArXiv
Analysis
This paper addresses the important problem of simplifying spatial graphs while preserving their topological structure. This is crucial for applications where the spatial relationships and overall structure are essential, such as in transportation networks or molecular modeling. The use of topological descriptors, specifically persistent diagrams, is a novel approach to guide the graph reduction process. The parameter-free nature and equivariance properties are significant advantages, making the method robust and applicable to various spatial graph types. The evaluation on both synthetic and real-world datasets further validates the practical relevance of the proposed approach.
Key Takeaways
- •Proposes a novel approach for spatial graph reduction.
- •Employs topological descriptors (persistent diagrams) to guide the reduction.
- •The method is parameter-free and equivariant.
- •Demonstrates effectiveness on both synthetic and real-world data.
Reference
“The coarsening is realized by collapsing short edges. In order to capture the topological information required to calibrate the reduction level, we adapt the construction of classical topological descriptors made for point clouds (the so-called persistent diagrams) to spatial graphs.”