Related papers: Nullspace embeddings for outerplanar graphs
A total weighting of a graph $G$ is a mapping $f$ which assigns to each element $z \in V(G) \cup E(G)$ a real number $f(z)$ as its weight. The vertex sum of $v$ with respect to $f$ is $\phi_f(v)=\sum_{e \in E(v)}f(e)+f(v)$. A total…
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
A subgraph $G'$ of a graph $G$ is nice if $G-V(G')$ has a perfect matching. Nice subgraphs play a vital role in the theory of ear decomposition and matching minors of matching covered graphs. A vertex $u$ of a cubic graph is nice if $u$ and…
Representation learning for graphs enables the application of standard machine learning algorithms and data analysis tools to graph data. Replacing discrete unordered objects such as graph nodes by real-valued vectors is at the heart of…
Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges…
The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms…
We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…
Graph representation learning models aim to represent the graph structure and its features into low-dimensional vectors in a latent space, which can benefit various downstream tasks, such as node classification and link prediction. Due to…
A rectangle visibility representation (RVR) of a graph consists of an assignment of axis-aligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its…
In a graph $G$, a vertex dominates itself and its neighbors. A subset $S\subseteq V(G)$ is said to be a double dominating set of $G$ if $S$ dominates every vertex of $G$ at least twice. The double domination number $\gamma_{\times 2}(G)$ is…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
We consider general integrable systems on graphs as discrete flat connections with the values in loop groups. We argue that a certain class of graphs is of a special importance in this respect, namely quad-graphs, the cellular…
This tutorial covers a few recent papers in the field of network embedding. Network embedding is a collective term for techniques for mapping graph nodes to vectors of real numbers in a multidimensional space. To be useful, a good embedding…
A realization of a graph $G=(V,E)$ is a map $v\colon V\to\Bbb R^d$ that assigns to each vertex a point in $d$-dimensional Euclidean space. We study graph realizations from the perspective of representation theory (expressing certain…
In this contribution, we demonstrate that Graph Neural Networks and Transformers can learn to reason about geometric constraints. We train them to predict spatial position of points in a discrete 2D grid from a set of constraints that…
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…
We consider embeddings of 3-regular graphs into 3-dimensional Cartesian coordinates, in such a way that two vertices are adjacent if and only if two of their three coordinates are equal (that is, if they lie on an axis-parallel line) and…
Weak unit disk contact graphs are graphs that admit representing nodes as a collection of internally disjoint unit disks whose boundaries touch if there is an edge between the corresponding nodes. In this work we focus on graphs without…