相关论文: Toward a Unit Distance Embedding for the Heawood g…

A directed graph $G$ is upward planar if it admits a planar embedding such that each edge is $y$-monotone. Unlike planarity testing, upward planarity testing is NP-hard except in restricted cases, such as when the graph has the…

Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

Graph embedding is a powerful method in parallel computing that maps a guest network $G$ into a host network $H$. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion and the…

Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…

We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named…

Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…

We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem---to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph---and…

Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…

It is known that graphs cellularly embedded into surfaces are equivalent to ribbon graphs. In this work, we generalize this statement to broader classes of graphs and surfaces. Half-edge graphs extend abstract graphs and are useful in…

A* is a classic and popular method for graphs search and path finding. It assumes the existence of a heuristic function $h(u,t)$ that estimates the shortest distance from any input node $u$ to the destination $t$. Traditionally, heuristics…

Entity alignment aims to match identical entities across different knowledge graphs (KGs). Graph neural network-based entity alignment methods have achieved promising results in Euclidean space. However, KGs often contain complex…

We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.

We prove that a graph has an infinitesimally rigid placement in a non-Euclidean normed plane if and only if it contains a $(2,2)$-tight spanning subgraph. The method uses an inductive construction based on generalised Henneberg moves and…

The $n$-$book ~embedding$ of a graph $G$ is an embedding of the graph $G$ in an $n$-book with the vertices of $G$ on the spine and each edge to the pages without crossing each other. If the degree of vertices of $G$ at most one in each…

The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in…

We prove that circle graphs (intersection graphs of circle chords) can be embedded as intersection graphs of rays in the plane with polynomial-size bit complexity. We use this embedding to show that the global curve simplification problem…

For a finite point set $E\subset \mathbb{R}^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k + 1$ points in E such that the distance between a pair of points is specified if the…

Recent studies have experimentally shown that we can achieve in non-Euclidean metric space effective and efficient graph embedding, which aims to obtain the vertices' representations reflecting the graph's structure in the metric space.…