arXiv:2607. 06646v1 Announce Type: cross Abstract: This paper introduces Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW), a novel method for graph comparison that unifies node features and structural connectivity through optimal transport.
arXiv:2203. 04711v2 Announce Type: replace Abstract: We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem.
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
arXiv:2606. 08258v1 Announce Type: cross Abstract: Understanding and comparing structures in scalar fields is a central challenge in scientific visualization, with applications ranging from feature analysis to temporal and structural comparison.
arXiv:2607. 16178v1 Announce Type: cross Abstract: In many applications of matching, the point clouds to be matched are not merely unstructured sets of points but rather samples from distributions with an intrinsic cluster structure.
arXiv:2608. 16923v1 Announce Type: cross Abstract: Networks provide a fundamental representation of relationships among entities.
arXiv:2606. 10295v1 Announce Type: cross Abstract: The Gromov--Wasserstein (GW) distance provides a framework for comparing metric measure spaces, regardless of their underlying structure or geometry.
arXiv:2608. 00621v1 Announce Type: new Abstract: Multimodal-attributed graphs (MAGs), whose nodes carry heterogeneous attributes such as text and images over a relational structure, have become a fundamental substrate for label-free entity grouping tasks, including community discovery and product segmentation.
arXiv:2607. 14880v1 Announce Type: cross Abstract: We propose a novel measure of the discrepancy between two probability distributions $f$ and $g$ on a graph - which we call the diffusion distance - that measures the rate of convergence of $f$ to $g$ under a graph-constrained Markov chain with stationary distribution $g$.
arXiv:2606. 18267v1 Announce Type: cross Abstract: Benchmarking shortest-path algorithms is commonly based on aggregate performance over heterogeneous graph sets, which limits insight into how different search paradigms react to instance structure.
arXiv:2507. 14484v2 Announce Type: replace Abstract: In recent years, graph neural networks (GNN) have achieved unprecedented successes in node classification tasks.
arXiv:2606. 15482v1 Announce Type: cross Abstract: Ricci flow is a curvature-guided diffusion process that deforms space by shrinking regions of high positive curvature and expanding those with negative curvature.
arXiv:2606. 19185v1 Announce Type: new Abstract: The Traveling Salesman Problem (TSP) is a cornerstone of combinatorial optimization and arises in many practical scenarios.