Related papers: Strongly Hyperbolic Unit Disk Graphs
A common way to accelerate shortest path algorithms on graphs is the use of a bidirectional search, which simultaneously explores the graph from the start and the destination. It has been observed recently that this strategy performs…
It is known that non-isomorphic strongly regular graphs with the same parameters must be cospectral (have the same eigenvalues). In this paper, we investigate whether the spectra of higher order Laplacians associated with these graphs can…
Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric…
Hyperbolic networks have shown prominent improvements over their Euclidean counterparts in several areas involving hierarchical datasets in various domains such as computer vision, graph analysis, and natural language processing. However,…
This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various `nonpositive…
Many high-dimensional practical data sets have hierarchical structures induced by graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional embeddings in other space forms to perform…
Capturing associations for knowledge graphs (KGs) through entity alignment, entity type inference and other related tasks benefits NLP applications with comprehensive knowledge representations. Recent related methods built on Euclidean…
The goal of this mostly expository paper is to present several candidates for hyperbolic structures on irreducible Artin-Tits groups of spherical type and to elucidate some relations between them. Most constructions are algebraic analogues…
Knowledge graph embeddings (KGE) have been validated as powerful methods for inferring missing links in knowledge graphs (KGs) that they typically map entities into Euclidean space and treat relations as transformations of entities.…
Chaotic hyperbolic dynamical systems enjoy a surprising degree of rigidity, a fact which is well known in the mathematics community but perhaps less so in theoretical physics circles. Low-dimensional hyperbolic systems are either conjugate…
We study the large-scale geometry of graph braid groups $\mathbb{B}_n(\mathsf{\Gamma})$, viewed as the fundamental groups of discrete configuration spaces $UD_n(\mathsf{\Gamma})$, which are special cube complexes in the sense of…
Graph embedding techniques have attracted growing interest since they convert the graph data into continuous and low-dimensional space. Effective graph analytic provides users a deeper understanding of what is behind the data and thus can…
Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…
We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, the automorphism group of the graph is compact-by-discrete.…
A constructive characterization of the class of uniformly $4$-connected graphs is presented. The characterization is based on the application of graph operations to appropriate vertex and edge sets in uniformly $4$-connected graphs, that…
Temporal link prediction, aiming to predict future edges between paired nodes in a dynamic graph, is of vital importance in diverse applications. However, existing methods are mainly built upon uniform Euclidean space, which has been found…
In this book authors for the first time introduce the notion of strong neutrosophic graphs. They are very different from the usual graphs and neutrosophic graphs. Using these new structures special subgraph topological spaces are defined.…
Learning the representation of data with hierarchical structures in the hyperbolic space attracts increasing attention in recent years. Due to the constant negative curvature, the hyperbolic space resembles tree metrics and captures the…
We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Dirichlet energy harmonic embedding of the graph among a fixed…
Bitcoin transaction networks are large scale socio- technical systems in which activities are represented through multi-hop interaction patterns. Graph Neural Networks(GNNs) have become a widely adopted tool for analyzing such systems,…