Related papers: Embedding Graphs into the Extended Grid

Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…

Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…

The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. These methods allow non-native problems to be adapted to the target annealer's architecture. The…

Despite the recent success of reconciling spike-based coding with the error backpropagation algorithm, spiking neural networks are still mostly applied to tasks stemming from sensory processing, operating on traditional data structures like…

We prove that there is a randomized polynomial-time algorithm that given an edge-weighted graph $G$ excluding a fixed-minor $Q$ on $n$ vertices and an accuracy parameter $\varepsilon>0$, constructs an edge-weighted graph~$H$ and an…

Graph embedding approaches attempt to project graphs into geometric entities, i.e, manifolds. The idea is that the geometric properties of the projected manifolds are helpful in the inference of graph properties. However, if the choice of…

This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…

The concept of graph flattenability, initially formalized by Belk and Connelly and later expanded by Sitharam and Willoughby, extends the question of embedding finite metric spaces into a given normed space. A finite simple graph $G=(V,E)$…

Machine learning on graph-structured data has recently become a major topic in industry and research, finding many exciting applications such as recommender systems and automated theorem proving. We propose an energy-based graph embedding…

Despite the enormous success of graph neural networks (GNNs), most existing GNNs can only be applicable to undirected graphs where relationships among connected nodes are two-way symmetric (i.e., information can be passed back and forth).…

Let $G=(V,E)$ be a bipartite graph embedded in a plane (or $n$-holed torus). Two subgraphs of $G$ differ by a {\it $Z$-transformation} if their symmetric difference consists of the boundary edges of a single face---and if each subgraph…

Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis…

A directed acyclic graph G = (V, E) is pseudo-transitive with respect to a given subset of edges E1, if for any edge ab in E1 and any edge bc in E, we have ac in E. We give algorithms for computing longest chains and demonstrate geometric…

In order to facilitate the accesses of general users to knowledge graphs, an increasing effort is being exerted to construct graph-structured queries of given natural language questions. At the core of the construction is to deduce the…

A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of…

Knowledge graph (KG) embedding aims at learning the latent representations for entities and relations of a KG in continuous vector spaces. An empirical observation is that the head (tail) entities connected by the same relation often share…

Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design…

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…

In the Flow Edge-Monitor Problem, we are given an undirected graph G=(V,E), an integer k > 0 and some unknown circulation \psi on G. We want to find a set of k edges in G, so that if we place k monitors on those edges to measure the flow…

Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved),…