Efficiently drawing a significant spanning tree of a directed graph

Martin Harrigan, Patrick Healy

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A directed graph can model any ordered relationship between objects. However, visualizing such graphs can be a challenging task. If the graph is undirected, a popular strategy is to choose a significant spanning tree, nominate a vertex as the root, for example the vertex whose distance from all other vertices is minimal, hang the significant spanning subtrees from this root and add in the remaining edges in some unobtrusive manner [18, 19, 25, 13]. In the directed case the spanning tree is a tree DAG (a directed graph without any undirected cycles) and not simply a directed tree with one appropriate root. It may have multiple sources (vertices with indegree equal to zero) that all warrant root status and so the undirected approach must be modified somewhat. In this paper, we present a method of drawing directed graphs that emphasizes a significant spanning tree. It can be considered a variation of the Sugiyama framework [23] in that it combines two steps of the framework (leveling and crossing minimisation) by finding, in linear time, a leveling of the graph that is level planar with respect to some spanning tree and restricting the permutations of the vertices on each level to those that constitute a level planar embedding of this subgraph. The edges of the spanning tree will therefore not cross each other. Using the globally oriented Fiedler vector we choose permutations of the vertices on each level that reduce the number of crossings between the remaining edges.

Original languageEnglish
Title of host publicationAsia-Pacific Symposium on Visualisation 2007, APVIS 2007, Proceedings
Pages53-59
Number of pages7
DOIs
Publication statusPublished - 2007
Event6th Asia-Pacific Symposium on Visualisation 2007, APVIS 2007 - Sydney, NSW, Australia
Duration: 5 Feb 20077 Feb 2007

Publication series

NameAsia-Pacific Symposium on Visualisation 2007, APVIS 2007, Proceedings

Conference

Conference6th Asia-Pacific Symposium on Visualisation 2007, APVIS 2007
Country/TerritoryAustralia
CitySydney, NSW
Period5/02/077/02/07

Keywords

  • Fiedler vector
  • Graph drawing
  • Level planarity
  • Significant spanning tree

Fingerprint

Dive into the research topics of 'Efficiently drawing a significant spanning tree of a directed graph'. Together they form a unique fingerprint.

Cite this