Related papers: Various Properties of Various Ultrafilters, Variou…

Large graphs can be found in a wide array of scientific fields ranging from sociology and biology to scientometrics and computer science. Their analysis is by no means a trivial task due to their sheer size and complex structure. Such…

We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…

We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…

Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…

Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…

Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations,…

Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…

Control-flow graphs (CFGs) of structured programs are well known to exhibit strong sparsity properties. Traditionally, this sparsity has been modeled using graph parameters such as treewidth and pathwidth, enabling the development of faster…

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…

Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…

We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…

In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is…

In this paper we give a comprehensive presentation of the notions of filter base, filter and ultrafilter on single valued neutrosophic set and we investigate some of their properties and relationships. More precisely, we discuss properties…

Graph-structured data pervades domains such as social networks, biological systems, knowledge graphs, and recommender systems. While foundation models have transformed natural language processing, vision, and multimodal learning through…

A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…

This paper explores the applications and challenges of graph neural networks (GNNs) in processing complex graph data brought about by the rapid development of the Internet. Given the heterogeneity and redundancy problems that graph data…

From longitudinal biomedical studies to social networks, graphs have emerged as a powerful framework for describing evolving interactions between agents in complex systems. In such studies, after pre-processing, the data can be represented…

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…