Related papers: Embedding Graphs as Euclidean kNN-Graphs
We aim to find orientations of mixed graphs optimizing the total reachability, a problem that has applications in causality and biology. For given a digraph $D$, we use $P(D)$ for the set of ordered pairs of distinct vertices in $V(D)$ and…
Let $\mathcal{A}$ be a set of positive numbers. A graph $G$ is called an $\mathcal{A}$-embeddable graph in $\mathbb{R}^d$ if the vertices of $G$ can be positioned in $\mathbb{R}^d$ so that the distance between endpoints of any edge is an…
The study of (minimally) rigid graphs is motivated by numerous applications, mostly in robotics and bioinformatics. A major open problem concerns the number of embeddings of such graphs, up to rigid motions, in Euclidean space. We capture…
This work proposes a Physics-informed Neural Network framework with Graph Embedding (GPINN) to perform PINN in graph, i.e. topological space instead of traditional Euclidean space, for improved problem-solving efficiency. The method…
In recent years, tasks of machine learning ranging from image processing & audio/video analysis to natural language understanding have been transformed by deep learning. The data content in all these scenarios are expressed via Euclidean…
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 neural networks (GNNs) are deep learning models designed specifically for graph data, and they typically rely on node features as the input to the first layer. When applying such a type of network on the graph without node features,…
k-nearest neighbor graph is a fundamental data structure in many disciplines such as information retrieval, data-mining, pattern recognition, and machine learning, etc. In the literature, considerable research has been focusing on how to…
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…
Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…
A graph is $d$-rigid if for any generic realisation of the graph in $\mathbb{R}^d$ (equivalently, the $d$-dimensional sphere $\mathbb{S}^d$), there are only finitely many non-congruent realisations in the same space with the same edge…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
A stable smooth map $f:N\to M$ is called "$k$-realizable" if its composition with the inclusion $M\subset M\times\Bbb R^k$ is $C^0$-approximable by smooth embeddings; and a "$k$-prem" if the same composition is $C^\infty$-approximable by…
Knowledge Graph(KG) has gained traction as a machine-readable organization of real-world knowledge for analytics using artificial intelligence systems. Graph Neural Network(GNN), is proven to be an effective KG embedding technique that…
Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have…
Let $G_n$ be a random geometric graph with vertex set $[n]$ based on $n$ i.i.d.\ random vectors $X_1,\ldots,X_n$ drawn from an unknown density $f$ on $\R^d$. An edge $(i,j)$ is present when $\|X_i -X_j\| \le r_n$, for a given threshold…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…
Learning node embeddings that capture a node's position within the broader graph structure is crucial for many prediction tasks on graphs. However, existing Graph Neural Network (GNN) architectures have limited power in capturing the…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…