Related papers: Embedded-Graph Theory
In this paper, we propose a novel edge-editing approach to extract relation information from a document. We treat the relations in a document as a relation graph among entities in this approach. The relation graph is iteratively constructed…
Federated graph learning collaboratively learns a global graph neural network with distributed graphs, where the non-independent and identically distributed property is one of the major challenges. Most relative arts focus on traditional…
In many domains (e.g. Internet of Things, neuroimaging) signals are naturally supported on graphs. These graphs usually convey information on similarity between the values taken by the signal at the corresponding vertices. An interest of…
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
Node similarity is a fundamental problem in graph analytics. However, node similarity between nodes in different graphs (inter-graph nodes) has not received a lot of attention yet. The inter-graph node similarity is important in learning a…
Most of the existing graph embedding methods focus on nodes, which aim to output a vector representation for each node in the graph such that two nodes being "close" on the graph are close too in the low-dimensional space. Despite the…
Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge…
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and…
The objective of knowledge graph embedding is to encode both entities and relations of knowledge graphs into continuous low-dimensional vector spaces. Previously, most works focused on symbolic representation of knowledge graph with…
In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose…
Graph embedding is the task of representing nodes of a graph in a low-dimensional space and its applications for graph tasks have gained significant traction in academia and industry. The primary difference among the many recently proposed…
Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges…
The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…
We describe recent achievements in the theory of weight systems, which are functions on chord diagrams satisfying so-called $4$-term relations. Our main attention is devoted to constructions of weight systems. The two main sources of these…
Given a connected graph $G(V, E)$, the edge dimension, denoted $\mathrm{edim}(G)$, is the least size of a set $S \subseteq V$ that distinguishes every pair of edges of $G$, in the sense that the edges have pairwise distinct tuples of…
In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…
Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. D\'enes proved that the permutation is a full cyclic permutation…