Related papers: Complex hypergraphs
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…
We present HoloGraphs, a novel approach for physically representing, explaining, exploring, and interacting with dynamic networks. HoloGraphs addresses the challenges of visualizing and understanding evolving network structures by providing…
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to…
We show that the core reasons that complex and hypercomplex valued neural networks offer improvements over their real-valued counterparts is the weight sharing mechanism and treating multidimensional data as a single entity. Their algebra…
To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed -- giving rise to different notions of width,…
We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and…
Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…
The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed -- giving rise to different notions of width,…
This article covers the problem of processing of Big Data that describe process of complex networks and network systems operation. It also introduces the notion of hierarchical network systems combination into associations and conglomerates…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
Modeling higher-order interactions (HOI) has emerged as a crucial challenge in complex systems analysis, as many phenomena cannot be fully captured by pairwise relationships alone. Hypergraphs, which generalize graphs by allowing…
There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…
Graphs serve as powerful tools for modeling pairwise interactions in diverse fields such as biology, material science, and social networks. However, they inherently overlook interactions involving more than two entities. Simplicial…
Many data sets, crucial for today's applications, consist essentially of enormous networks, containing millions or even billions of elements. Having the possibility of visualizing such networks is of paramount importance. We propose an…