Related papers: Algebraic methods for counting Euclidean embedding…
Knowledge graphs have emerged as fundamental structures for representing complex relational data across scientific and enterprise domains. However, existing embedding methods face critical limitations when modeling diverse relationship…
Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…
Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…
We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard…
We study $k$-page upward book embeddings ($k$UBEs) of $st$-graphs, that is, book embeddings of single-source single-sink directed acyclic graphs on $k$ pages with the additional requirement that the vertices of the graph appear in a…
Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): finding mappings of request graphs (describing the workloads) onto a substrate graph (describing the physical…
Rigid graphs have only finitely many realizations. In the recent years significant progress was made in computing the number of such realizations. With this progress it was also possible for the first time to do computations on large sets…
We classify rotary (orientably-regular) maps whose underlying graphs are multicycles. For the multicycle $\mathrm{C}_n^{(\lambda)}$ of length $n$ and edge-multiplicity $\lambda$, we determine all rotary embeddings for $n\geqslant 3$ and…
Graph Representation Learning (GRL) has experienced significant progress as a means to extract structural information in a meaningful way for subsequent learning tasks. Current approaches including shallow embeddings and Graph Neural…
We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the…
We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in…
We take an elementary and systematic approach to the problem of extending the Tutte polynomial to the setting of embedded graphs. Four notions of embedded graphs arise naturally when considering deletion and contraction operations on graphs…
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…
In this paper, two results are obtained on a hypergraph embedding problem. The proof technique is itself of interest, being the first time amalgamations have been used to address the embedding of hypergraphs. The first result finds…
A fundamental theorem of Laman characterises when a bar-joint framework realised generically in the Euclidean plane admits a non-trivial continuous deformation of its vertices. This has recently been extended in two ways. Firstly to…
Machine learning, deep learning, and NLP methods on knowledge graphs are present in different fields and have important roles in various domains from self-driving cars to friend recommendations on social media platforms. However, to apply…
We give a series of new lower bounds on the minimum number of vertices required by a graph to contain every graph of a given family as induced subgraph. In particular, we show that this induced-universal graph for $n$-vertex planar graphs…