Diagram editors which are tailored to a specific diagram language typically support either syntax-directed editing or free-hand editing, i.e., the user is either restricted to a collection of predefined editing operations, or he is not restricted at all, but misses the convenience of such complex editing operations. This paper proposes a concept for incorporating both modes into one editor in o...

Diagrams that serve as a visual input facility for programming environments have to be translated into some kind of semantic description. This paper describes such a method which is based on a specification of the translation process. The translation process starts with a diagram, which is simply represented as a collection of atomic diagram components, and it ends up with some data structure a...

When working with diagrams in visual environments like graphical diagram editors, diagrams have to be represented by an internal model. Graphs and hypergraphs are well-known concepts for such internal models. This paper shows how hypergraphs can be uniformly used for a wide range of different diagram types where hyperedges are used to represent diagram components as well as spatial relationship...

Sketching, i.e., drawing diagrams by hand and directly on the screen, is gaining popularity, as it is a comfortable and natural way to create and edit diagrams. Hand drawing is inherently imprecise, and often sloppy. As a consequence, when processing hand drawn diagrams with a computer, ambiguities arise: it is not always clear what part of the drawing is meant to represent what component. Reso...

DiaGen is a specification method, which is primarily based on a hypergraph grammar, and a tool that allows to automatically generate diagram editors from such a specification. Generated editors are free-hand editors, but with an automatic, constraint-based layout for correct diagrams. A hypergraph parser checks diagram correctness and makes it possible to translate diagrams into some user-defin...

Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms assumed pairwise relationships objects interest. However, many real applications, the between are higher-order, beyond a formulation. To efficiently learn deep embeddings on high-order graph-structured data, we introduce two end-to-end trainable ...

for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.

In this paper, we introduce certain concepts, including neutrosophic hypergraph, line graph of neutrosophic hypergraph, dual neutrosophic hypergraph, tempered neutrosophic hypergraph and transversal neutrosophic hypergraph. We illustrate these concepts by several examples and investigate some of interesting properties. Key-words: Neutrosophic hypergraph, Line graph of neutrosophic hypergraph, D...

Abstract This chapter introduces three hypergraph computation paradigms, including intra-hypergraph computation, inter-hypergraph and structure computation. Intra-hypergraph representation aims to conduct learning of a hypergraph, where each subject is represented by its components. Inter-hypergraph vertices in the vertex hypergraph. Hypergraph prediction, which find connections among vertices....

In this paper, the concept of hypergraph is extended to the fuzzy hypergraph. In the fuzzy hypergraph, the concepts of a-cut hypergraph, strength of edge and dual fuzzy hypergraph are developed. It is shown that the fuzzy hypergraph and a-cut hypergraph are useful to represent a fuzzy partition. An application example also shows that the strength of edge can be used to decompose the data set in...