Article

# Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs

National ICT Australia Australia; School of Computer Science and Engineering, University of New SouthWales, Sydney,NSW2052 Australia Australia

Algorithmica (Impact Factor: 0.49). 12/2005; 44(1):1-32. DOI: 10.1007/s00453-004-1144-8 Source: CiteSeer

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**ABSTRACT:**Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in VLSI de- sign, CASE tools, software visualisation and visualisation of social networks and bi- ological networks. Straight-line drawing algorithms for hierarchical graphs and clus- tered graphs have been presented in (P. Eades, Q. Feng, X. Lin and H. Nagamochi, Straight-line drawing algorithms for hierarchical graphs and clustered graphs, Algo- rithmica, 44, pp. 1-32, 2006). A straight-line drawing is called a convex drawing if every facial cycle is drawn as a convex polygon. In this paper, it is proved that every internally triconnected hierarchical plane graph with the outer facial cycle drawn as a convex polygon admits a convex drawing. We present an algorithm which constructs such a drawing. We then extend our results to convex representations of clustered planar graphs. It is proved that every internally triconnected clustered plane graph with completely connected clustering structure admits a convex drawing. We present an algorithm to construct a convex drawing of clustered planar graphs.J. Discrete Algorithms. 01/2010; 8:282-295. - [Show abstract] [Hide abstract]

**ABSTRACT:**Graph visualization has been widely used to understand and present both global structural and local adjacency information in relational data sets (e.g., transportation networks, citation networks, or social networks). Graphs with dense edges, however, are difficult to visualize because fast layout and good clarity are not always easily achieved. When the number of edges is large, edge bundling can be used to improve the clarity, but in many cases, the edges could be still too cluttered to permit correct interpretation of the relations between nodes. In this paper, we present an ambiguity-free edge-bundling method especially for improving local detailed view of a complex graph. Our method makes more efficient use of display space and supports detail-on-demand viewing through an interactive interface. We demonstrate the effectiveness of our method with public coauthorship network data.IEEE transactions on visualization and computer graphics. 05/2012; 18(5):810-21. - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper proposes an organized generalization of Newman and Girvan's modularity measure for graph clustering. Optimized via a deterministic annealing scheme, this measure produces topologically ordered graph clusterings that lead to faithful and readable graph representations based on clustering induced graphs. Topographic graph clustering provides an alternative to more classical solutions in which a standard graph clustering method is applied to build a simpler graph that is then represented with a graph layout algorithm. A comparative study on four real world graphs ranging from 34 to 1133 vertices shows the interest of the proposed approach with respect to classical solutions and to self-organizing maps for graphs.Neurocomputing. 01/2010;

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