{"title":"Efficiently drawing a significant spanning tree of a directed graph","authors":"Martin Harrigan, P. Healy","doi":"10.1109/APVIS.2007.329275","DOIUrl":"https://doi.org/10.1109/APVIS.2007.329275","url":null,"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. 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 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.","PeriodicalId":136557,"journal":{"name":"2007 6th International Asia-Pacific Symposium on Visualization","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121599744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Buchsbaum, E. Gansner, Suresh Venkatasubramanian
{"title":"Directed graphs and rectangular layouts","authors":"A. Buchsbaum, E. Gansner, Suresh Venkatasubramanian","doi":"10.1109/APVIS.2007.329276","DOIUrl":"https://doi.org/10.1109/APVIS.2007.329276","url":null,"abstract":"This paper deals with the problem, arising in practice, of drawing a directed graph as a collection of disjoint, isothetic rectangles, where the rectangles of the nodes of each edge must touch and where the placement of the rectangles respects the ordering of the edges. It provides characterizations for those graphs having the special type of rectangular layout known as a rectangular dual. It then characterizes the st-graphs having rectangular layouts in terms of the existence of certain planar embeddings and the non-existence of a particular subgraph.","PeriodicalId":136557,"journal":{"name":"2007 6th International Asia-Pacific Symposium on Visualization","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127523628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Force-directed drawing method for intersecting clustered graphs","authors":"H. Omote, Kozo Sugiyama","doi":"10.1109/APVIS.2007.329280","DOIUrl":"https://doi.org/10.1109/APVIS.2007.329280","url":null,"abstract":"We present a novel force-directed method for drawing an intersecting clustered graph. This is based upon simulation of a virtual physical system. The graph can express complicated structures such as inclusion and intersection between vertices/clusters as well as adjacency, and it is used in diverse fields such as creativity support, software engineering, and semantic Web. We describe definitions, aesthetics, model, algorithm, performance evaluation, and applications.","PeriodicalId":136557,"journal":{"name":"2007 6th International Asia-Pacific Symposium on Visualization","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121074844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}