Topological Spatial Graph Coarsening
Anna Calissano, Etienne Lasalle

TL;DR
This paper introduces a novel, parameter-free method for reducing spatial graphs by collapsing short edges while preserving topological features, using a new filtration based on persistent diagrams, and proves its invariance under geometric transformations.
Contribution
It presents a topological spatial graph coarsening framework that balances graph reduction with topological preservation, utilizing a new triangle-aware filtration and proving geometric invariance.
Findings
Significantly reduces graph size while maintaining topological features
Effective on both synthetic and real spatial graphs
Parameter-free and invariant under geometric transformations
Abstract
Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to find a smaller spatial graph (i.e., with less nodes) with the same overall structure as the initial one. In this context, performing the graph reduction while preserving the main topological features of the initial graph is particularly relevant, due to the additional spatial information. Thus, we propose a topological spatial graph coarsening approach based on a new framework that finds a trade-off between the graph reduction and the preservation of the topological characteristics. 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…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Advanced Graph Neural Networks · Graph Theory and Algorithms
