Related papers: Strongly Hyperbolic Unit Disk Graphs
Graph convolutional networks (GCNs) have received considerable research attention recently. Most GCNs learn the node representations in Euclidean geometry, but that could have a high distortion in the case of embedding graphs with…
Learning generalizable self-supervised graph representations for downstream tasks is challenging. To this end, Contrastive Learning (CL) has emerged as a leading approach. The embeddings of CL are arranged on a hypersphere where similarity…
A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for \textsc{Maximum Clique} on unit disk graphs [Clark, Colbourn, Johnson; Discrete…
Graph clustering has been popularly studied in recent years. However, most existing graph clustering methods focus on node-level clustering, i.e., grouping nodes in a single graph into clusters. In contrast, graph-level clustering, i.e.,…
Hyperbolic space can naturally embed hierarchies, unlike Euclidean space. Hyperbolic Neural Networks (HNNs) exploit such representational power by lifting Euclidean features into hyperbolic space for classification, outperforming Euclidean…
Knowledge graphs have emerged as fundamental structures for representing complex relational data across scientific and enterprise domains. However, existing embedding methods face critical limitations when modeling diverse relationship…
Unigraphs are graphs uniquely determined by their own degree sequence up to isomorphism. There are many subclasses of unigraphs such as threshold graphs, split matrogenic graphs, matroidal graphs, and matrogenic graphs. Unigraphs and these…
Generative network models play an important role in algorithm development, scaling studies, network analysis, and realistic system benchmarks for graph data sets. The commonly used graph-based benchmark model R-MAT has some drawbacks…
\"Uberhomology is a recently defined homology theory for simplicial complexes, which yields subtle information on graphs. We prove that bold homology, a certain specialisation of \"uberhomology, is related to dominating sets in graphs. To…
Hyperbolic representations are effective in modeling knowledge graph data which is prevalently used to facilitate multi-hop reasoning. However, a rigorous and detailed comparison of the two spaces for this task is lacking. In this paper,…
The class of quasi-median graphs is a generalisation of median graphs, or equivalently of CAT(0) cube complexes. The purpose of this thesis is to introduce these graphs in geometric group theory. In the first part of our work, we extend the…
We explore two properties of backward orbits under semigroups of holomorphic self-maps in the unit disk. First, we prove that regular backward orbits are quasi-geodesics for the hyperbolic distance of the unit disk. Then, we show that…
Functional magnetic resonance imaging (fMRI) reveals complex brain functional networks with hierarchical topologies crucial for cognitive processing. Standard Euclidean Graph Neural Networks (GNNs) often struggle to represent these…
Data with geometric structure is ubiquitous in machine learning often arising from fundamental symmetries in a domain, such as permutation-invariance in graphs and translation-invariance in images. Group-convolutional architectures, which…
Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…
We describe an efficient method for drawing any n-vertex simple graph G in the hyperbolic plane. Our algorithm produces greedy drawings, which support greedy geometric routing, so that a message M between any pair of vertices may be routed…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
The recent reconstruction of the Drosophila brain provides a neural network of unprecedented size and level of details. In this work, we study the geometrical properties of this system by applying network embedding techniques to the graph…
Graph-structured data provide a comprehensive description of complex systems, encompassing not only the interactions among nodes but also the intrinsic features that characterize these nodes. These features play a fundamental role in the…
Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is…