Related papers: Some graph theoretical aspects of generalized trun…

Message-passing graph neural networks (MPNNs) have emerged as the leading approach for machine learning on graphs, attracting significant attention in recent years. While a large set of works explored the expressivity of MPNNs, i.e., their…

To each colored graph, one can associate its closure in the universal space of isomorphism classes of pointed colored graphs, and this subspace can be regarded as a generalized subshift. Based on this correspondence, we extend the notion of…

We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.

Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…

Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or…

In a bidirected graph an edge has a direction at each end, so bidirected graphs generalize directed graphs. We generalize the definitions of transitive closure and transitive reduction from directed graphs to bidirected graphs by…

By defining grids as graphs, geometric graphs can be represented in a very concise way.

In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.

Ontologies have been widely used in numerous and varied applications, e.g., to support data modeling, information integration, and knowledge management. With the increasing size of ontologies, ontology understanding, which is playing an…

We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.

Hypergraphs, as a generalization of simplicial complexes, have long been a subject of interest in their geometric interpretation. The subdivision of simplicial complexes can, to some extent, provide insights into the geometry of simplicial…

We give a brief survey of some known results on intrinsically linked or knotted graphs.

One of the hot topics in machine learning is the field of GNN. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph…

Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…

We present an informal survey (meant to accompany another paper) on graph compression methods. We focus on lossless methods, briefly list available pproaches, and compare them where possible or give some indicators on their compression…

Machine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across a broad spectrum of disciplines, from life to social and engineering sciences. Despite…

The definition of edge-regularity in graphs is a relaxation of the definition of strong regularity, so strongly regular graphs are edge-regular and, not surprisingly, the family of edge-regular graphs is much larger and more diverse than…

Graphons are limit objects of sequences of graphs and are used to analyze the behavior of large graphs. Recently, graphon signal processing has been developed to study signal processing on large graphs. A major limitation of this approach…

In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…

We study topological properties of the graph topology.