Related papers: (c-)AND: A new graph model
Context: Edge graphs are graphs whose edges are labelled with identifiers, and nodes can have multiple edges between them. They are used to model a wide range of systems, including networks with distances or degrees of connection and…
In this paper, we study orthogonal representations of simple graphs $G$ in $\mathbb{R}^d$ from an algebraic perspective in case $d = 2$. Orthogonal representations of graphs, introduced by Lov\'asz, are maps from the vertex set to…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…
We investigate properties which ensure that a given finite graph is the commuting graph of a group or semigroup. We show that all graphs on at least two vertices such that no vertex is adjacent to all other vertices is the commuting graph…
An \emph{obstacle representation} of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent. Obstacle representations…
We classify a class of complex representations of an arbitrary Coxeter group via characters of the integral homology of certain graphs. Such representations can be viewed as a generalization of the geometric representation and correspond to…
We introduce a graph-theoretic vertex dissolution model that applies to a number of redistribution scenarios such as gerrymandering in political districting or work balancing in an online situation. The central aspect of our model is the…
Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed…
Let $S$ be a set of $n$ points in the plane in general position. Two line segments connecting pairs of points of $S$ cross if they have an interior point in common. Two vertex disjoint geometric graphs with vertices in $S$ cross if there…
An independent set may not contain both a vertex and one of its neighbours. This basic fact makes the uniform distribution over independent sets rather special. We consider the hard-core model, an essential generalization of the uniform…
In order to make graphical Gaussian models a viable modelling tool when the number of variables outgrows the number of observations, model classes which place equality restrictions on concentrations or partial correlations have previously…
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,…
Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…
Learning universal graph representations across heterogeneous domains is difficult because graph datasets differ in topology, node-attribute semantics, feature dimensions, and even attribute availability. We propose GraphVec, a…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…
In this paper, we introduce a matrix for a mixed graph, called the integrated adjacency matrix. This matrix uniquely determines a mixed graph, as long as the indices of the matrix are specified. Additionally, we associate an (undirected)…
A graph $G=(V,E)$ is word-representable if and only if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$, $x\neq y$, alternate in $w$ if and only if $xy\in E$. A split graph is a graph in which the vertices can be…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…