Related papers: Folding and Unfolding on Metagraphs
Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…
Existing foundation models, such as CLIP, aim to learn a unified embedding space for multimodal data, enabling a wide range of downstream web-based applications like search, recommendation, and content classification. However, these models…
Hypergraphs generalize classical graphs by allowing a single edge to connect multiple vertices, providing a natural language for modeling higher-order interactions. Superhypergraphs extend this paradigm further by accommodating nested,…
Polygraphs are a higher-dimensional generalization of the notion of directed graph. Based on those as unifying concept, this monograph on polygraphs revisits the theory of rewriting in the context of strict higher categories, adopting the…
Graphs and various graph-like combinatorial structures, such as preorders and hypergraphs, are ubiquitous in programming. This paper focuses on representing graphs in a purely functional programming language like Haskell. There are several…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
We consider a framework for clustering edge-colored hypergraphs, where the goal is to cluster (equivalently, to color) objects based on the primary type of multiway interactions they participate in. One well-studied objective is to color…
Target class classification is a mixed classification and transition model whose integrated goal is to assign objects to a certain, so called target or normal class. The classification process is iterative, and in each step an object in a…
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…
Graph minors are a primary tool in understanding the structure of undirected graphs, with many conceptual and algorithmic implications. We propose new variants of \emph{directed graph minors} and \emph{directed graph embeddings}, by…
The vast amount of data and increase of computational capacity have allowed the analysis of texts from several perspectives, including the representation of texts as complex networks. Nodes of the network represent the words, and edges…
We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we…
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…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles. In an academic collaboration network, for example,…
In this paper we study fundamental connectivity properties of hypergraphs from a graph-theoretic perspective, with the emphasis on cut edges, cut vertices, and blocks. To prepare the ground, we define various types of subhypergraphs, as…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…