Subdivision Drawings of Hypergraphs

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. This research was initiated during the Bertinoro Workshop on Graph Drawing, 2008. Bettina Speckmann is supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 639.022.707.

[1]  Anne Verroust-Blondet,et al.  Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets , 2004, Diagrams.

[2]  Timothy R. S. Walsh,et al.  Hypermaps versus bipartite maps , 1975 .

[3]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[4]  Emad Ramadan,et al.  A hypergraph model for the yeast protein complex network , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[5]  Hans-Jörg Kreowski,et al.  Formal Methods in Software and Systems Modeling, Essays Dedicated to Hartmut Ehrig, on the Occasion of His 60th Birthday , 2005, Formal Methods in Software and Systems Modeling.

[6]  Michael B. Dillencourt,et al.  Realizability of Delaunay Triangulations , 1990, Inf. Process. Lett..

[7]  Georg Sander,et al.  Layout of Directed Hypergraphs with Orthogonal Hyperedges , 2003, GD.

[8]  Erkki Mäkinen,et al.  How to draw a hypergraph , 1990, Int. J. Comput. Math..

[9]  John Howse,et al.  Generating Euler Diagrams , 2002, Diagrams.

[10]  Mary Jo Henning,et al.  The Electronic Text , 1990 .

[11]  Bernd Becker,et al.  Orthogonal Hypergraph Drawing for Improved Visibility , 2006, J. Graph Algorithms Appl..

[12]  David S. Johnson,et al.  Hypergraph planarity and the complexity of drawing venn diagrams , 1987, J. Graph Theory.

[13]  Michael Brinkmeier,et al.  Communities in graphs and hypergraphs , 2007, CIKM '07.

[14]  Ronald Fagin,et al.  Degrees of acyclicity for hypergraphs and relational database schemes , 1983, JACM.

[15]  J. Richard Lundgren,et al.  Food Webs, Competition Graphs, Competition-Common Enemy Graphs, and Niche Graphs , 1989 .

[16]  Peter Eades,et al.  Drawing Hypergraphs in the Subset Standard , 2000 .

[17]  Micha Sharir,et al.  Davenport-Schinzel sequences and their geometric applications , 1995, Handbook of Computational Geometry.

[18]  Peter Eades,et al.  Drawing Hypergraphs in the Subset Standard (Short Demo Paper) , 2000, GD.