The quality of an embedding Φ : V 7→ R of a graph G = (V, E) into the Euclidean plane is the ratio of max{u,v}∈E ||Φ(u) − Φ(v)||2 to min{u,v}6∈E ||Φ(u) − Φ(v)||2. Given a graph G = (V, E), that is known to be a unit ball graph in fixed dimensional Euclidean space R, we seek algorithms to compute an embedding Φ : V 7→ R of best (smallest) quality. Note that G comes with no associated geometric i...

In this paper, we prove that all Euclidean Artin–Tits groups are acylindrically hyperbolic. To any Garside group of finite type, Wiest and the author associated a hyperbolic graph called additional length they used it to show central quotients spherical type general, is not priori but McCammond Sulway have shown embeds into an infinite-type which call crystallographic group. We associate exhibi...

This paper describes how graph-spectral methods can be used to transform the node correspondence problem into one of point-set alignment. We commence by using the ISOMAP algorithm to embed the nodes of a graph in a low-dimensional Euclidean space. With the nodes in the graph transformed to points in a metric space, we can recast the problem of graph-matching into that of aligning the points. He...

Many machine learning algorithms for clustering or dimensionality reduction take as input a cloud of points in Euclidean space, and construct a graph with the input data points as vertices. This graph is then partitioned (clustering) or used to redefine metric information (dimensionality reduction). There has been much recent work on new methods for graph-based clustering and dimensionality red...

In this paper we propose an algorithm for automatic transformation of a graph into a 3D Virtual World and its Euclidean map, using the rectangular dualization technique. The nodes of the initial graph are transformed into rooms, the connecting arcs between nodes determine which rooms have to be placed next to each other and define the positions of the doors connecting those rooms. The proposed ...

Graph neural networks (GNNs) have developed rapidly in recent years because they can work over non-Euclidean data and possess promising prediction power many real-word applications. The graph classification problem is one of the central problems networks, aims to predict label a with help training graph-structural datasets. pooling scheme an important part for objective. Previous works typicall...

A minimal filling of a finite metric space is weighted graph possible weight spanning this so that the any path in it not less than distance between its ends. Bifurcation diagrams types and fillings for four points Euclidean plane are built present work.

Abstract We describe two mathematical representations for what have come to be called “semantic maps”, that is, of typological universals linguistic co-expression with the aim inferring similarity relations between concepts from those universals. The are a graph structure and Euclidean space, latter as inferred through multidimensional scaling. Graph in types. In both types, meanings represente...

Abstract. Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. A graph is a ...

Let $$n\geqslant 1$$ be a number. $${\Gamma }_n$$ the graph on $$\mathbb {R}^n$$ connecting points of rational Euclidean distance. It is consistent with choiceless set theory $$\textrm{ZF}\,{+}\,\textrm{DC}$$ that has countable chromatic number, yet number $$\Gamma _{n+1}$$ uncountable.