Related papers: Transformations on hypergraph families

Hypergraphs naturally represent higher-order interactions, which persistently appear from social interactions to neural networks and other natural systems. Although their importance is well recognized, a theoretical framework to describe…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

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…

Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large-scale complex flexible engineering systems. It does so by fusing concepts from network science and model-based systems…

In this paper, we introduce a method called graph fusion embedding, designed for multi-graph embedding with shared vertex sets. Under the framework of supervised learning, our method exhibits a remarkable and highly desirable synergistic…

Starting from context-free inverse graphs, we introduce a new class of groups and study their structural properties. We establish closure properties, show that their co-word problems are context-free, analyze torsion elements, and realize…

A connected 1-factorisation is a 1-factorisation of a hypergraph for which the union of each pair of distinct 1-factors is a connected hypergraph. A uniform 1-factorisation is a 1-factorisation of a hypergraph for which the union of each…

Hypergroups are lifted to power semigroups with negation, yielding a method of transferring results from semigroup theory. This applies to analogous structures such as hypergroups, hyperfields, and hypermodules, and permits us to transfer…

We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between…

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function…

We have established a coherent framework for applying variational methods to partial differential equations on hypergraphs, which includes the propositions of calculus and function spaces on hypergraphs. Several results related to the…

Graph burning is a round-based game or process that discretely models the spread of influence throughout a network. We introduce a generalization of graph burning which applies to hypergraphs, as well as a variant called ''lazy'' hypergraph…

In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such…

This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…

In this work we produce a framework for constructing universal function approximators on graph isomorphism classes. We prove how this framework comes with a collection of theoretically desirable properties and enables novel analysis. We…

Many applications of graph transformation require rules that change a graph without introducing new consistency violations. When designing such rules, it is natural to think about the desired outcome state, i.e., the desired effect, rather…

We introduce a hypergraph matrix, named the unified matrix, and use it to represent the hypergraph as a graph. We show that the unified matrix of a hypergraph is identical to the adjacency matrix of the associated graph. This enables us to…

We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…

Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…