Related papers: Ubergraphs: A Definition of a Recursive Hypergraph…
The independence polynomial of a hypergraph is the generating function for its independent (vertex) sets with respect to their cardinality. This article aims to discuss several recurrence relations for the independence polynomial using some…
In this paper we introduce a graph structure, called subspace sum graph $\mathcal{G}(\mathbb{V})$ on a finite dimensional vector space $\mathbb{V}$ where the vertex set is the collection of non-trivial proper subspaces of a vector space and…
Large knowledge graphs combine human knowledge garnered from projects ranging from academia and institutions to enterprises and crowdsourcing. Within such graphs, each relationship between two nodes represents a basic fact involving these…
The mathematical formalisms used to model biological systems induce both latent and ambiguous assumptions that can limit or distort their representational capabilities. Developing formalisms that can represent systems more precisely is…
We explore recursive programming with extensible data types. Row types make the structure of data types first class, and can express a variety of type system features including record subtyping and combination of case branches. Our goal is…
Complex networks can be used to analyze structures and systems in the embryo. Not only can we characterize growth and the emergence of form, but also differentiation. The process of differentiation from precursor cell populations to…
The hypergraph-of-entity was conceptually proposed as a general model for entity-oriented search. However, only the performance for ad hoc document retrieval had been assessed. We continue this line of research by also evaluating ad hoc…
We introduce certain lattice sums associated with hyperplane arrangements, which are (multiple) sums running over integers, and can be regarded as generalizations of certain linear combinations of zeta-functions of root systems. We also…
Hypergraphs are a generalized data structure of graphs to model higher-order correlations among entities, which have been successfully adopted into various research domains. Meanwhile, HyperGraph Neural Network (HGNN) is currently the…
A thesaurus is one, out of many, possible representations of term (or word) connectivity. The terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph. The directionality of the links retains all…
In the present paper we discuss the clustering procedure in the case where instead of a single metric we have a family of metrics. In this case we can obtain a partially ordered graph of clusters which is not necessarily a tree. We discuss…
There are different concepts regarding to tree decomposition of a graph $G$. For the Hypercube $Q_n$, these concepts have been shown to have many applications. But some diverse papers on this subject make it difficult to follow what is…
Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise…
Hypergraphs were introduced in 1973 by Berg\'e. This review aims at giving some hints on the main results that we can find in the literature, both on the mathematical side and on their practical usage. Particularly, different definitions of…
We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…
In this communication we propose the use of the Augmented Space Recursion as an ideal methodology for the study of electronic and magnetic structures of rough surfaces, interfaces and overlayers. The method can take into account roughness,…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
The Hales numbered $n$-dimensional hypercube and the corresponding adjacency matrix exhibit interesting recursive structures in $n$. These structures lead to a very simple proof of the well-known bandwidth formula for hypercube, whose proof…
For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. In addition to studying these matrices, several related structures are…
Several recent works have identified patterns that must exist in dense subsets of either the vertices or the edges of a large hypercube. We introduce a framework, based on the concept of series-parallel graphs, that unifies and generalizes…