How to draw a hypergraph

Mäkinen, Erkki

doi:10.1080/00207169008803875

Cited by 47 publications

(35 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Mäkinen (1990) introduced two notions of hypergraph drawing based on methods for describing a hypergraph: the subset standard and the edge standard. The first one uses the fact that a hypergraph is a collection of subsets, which can be viewed as a Venn diagram.…”

Section: If Every Hyperarc a ∈ A Is Such That |Dest(a)| = 1 Than H Ismentioning

confidence: 99%

See 1 more Smart Citation

Directed hypergraph planarity

Guedes

Markenzon

2005

Pesqui. Oper.

View full text Add to dashboard Cite

Directed hypergraphs are generalizations of digraphs and can be used to model binary relations among subsets of a given set. Planarity of hypergraphs was studied by Johnson and Pollak; in this paper we extend the planarity concept to directed hypergraphs. It is known that the planarity of a digraph relies on the planarity of its underlying graph. However, for directed hypergraphs, this property do not apply and we propose a new approach which generalizes the usual concept. We also show that the complexity of the recognition of a directed hypergraph as planar is linear on the size of the hypergraph.Keywords: directed hypergraphs; planarity; algorithms. ResumoHipergrafos direcionados são generalizações de digrafos, e são utilizados na modelagem de relações binárias entre subconjuntos de um dado conjunto. O problema da planaridade em hipergrafos foi estudado por Johnson e Pollak; neste trabalho estendemos o conceito de planaridade para hipergrafos direcionados. É noção conhecida que a planaridade de hipergrafos depende da planaridade de seu grafo subjacente. Entretanto, para hipergrafos direcionados, esta propriedade não pode ser aplicada e propomos uma nova abordagem que generaliza o conceito tradicional. Mostramos também que a complexidade de testar a planaridade de um hipergrafo direcionado é linear no tamanho do hipergrafo.Palavras-chave: hipergrafos direcionados; planaridade; algoritmos.

show abstract

Section: If Every Hyperarc a ∈ A Is Such That |Dest(a)| = 1 Than H Ismentioning

confidence: 99%

“…Planarity of hypergraphs was studied by Johnson & Pollak (1987) and their paper yields our theoretical approach. Mäkinen (1990) gives emphasis to the drawing of hypergraphs, where planarity plays an important role. He includes some remarks about directed hypergraph drawing, assuming a restricted definition.…”

Section: Introductionmentioning

confidence: 99%

Directed hypergraph planarity

Guedes

Markenzon

2005

Pesqui. Oper.

View full text Add to dashboard Cite

show abstract

“…An edge-based hypergraph drawing resembles standard drawings of graphs more closely [11]. Vertices are again drawn as points, but hyperedges are drawn as Steiner trees (see Fig.…”

Section: Introductionmentioning

confidence: 99%

Subdivision Drawings of Hypergraphs

2009

View full text Add to dashboard Cite

Abstract. We introduce the concept of subdivision drawings of hypergraphs. In a subdivision drawing each vertex corresponds uniquely to a face of a planar subdivision and, for each hyperedge, the union of the faces corresponding to the vertices incident to that hyperedge is connected. Vertex-based Venn diagrams and concrete Euler diagrams are both subdivision drawings. In this paper we study two new types of subdivision drawings which are more general than concrete Euler diagrams and more restricted than vertex-based Venn diagrams. They allow us to draw more hypergraphs than the former while having better aesthetic properties than the latter.

show abstract

“…(Bipartite) graphs are well-known mathematical objects which, as formal representation, have several advantages over the triple or directed labeled graph representation discussed above. Among these advantages are: algorithms for the visualization of data for humans [6,7], a formal framework to prove properties and specify algorithms, the availability of libraries with generic implementations of graph algorithms, and of course, techniques and results of graph theory. Representing RDF data by (standard) graphs allows to reduce application demands to well-studied problems of graphs.…”

Section: Introductionmentioning

confidence: 99%

Bipartite Graphs as Intermediate Model for RDF

Hayes

Gutiérrez

2004

The Semantic Web – ISWC 2004

104

113

View full text Add to dashboard Cite

Abstract. RDF Graphs are sets of assertions in the form of subjectpredicate-object triples of information resources. Although for simple examples they can be understood intuitively as directed labeled graphs, this representation does not scale well for more complex cases, particularly regarding the central notion of connectivity of resources. We argue in this paper that there is need for an intermediate representation of RDF to enable the application of well-established methods from graph theory. We introduce the concept of RDF Bipartite Graph and show its advantages as intermediate model between the abstract triple syntax and data structures used by applications. In the light of this model we explore the issues of transformation costs, data/schemastructure, and the notion of RDF connectivity.

show abstract

How to draw a hypergraph

Cited by 47 publications

References 13 publications

Directed hypergraph planarity

Directed hypergraph planarity

Subdivision Drawings of Hypergraphs

Bipartite Graphs as Intermediate Model for RDF

Contact Info

Product

Resources

About