Convex drawings of hierarchical planar graphs and clustered planar graphs

: Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in VLSI design, CASE tools, software visualisation and visualisation of social networks and biological networks. Straight-line drawing algorithms for hierarchical graphs and clustered graphs have been presented in [P. Eades, Q. Feng, X. Lin and H. Nagamochi, Straight-line drawing algorithms for hierarchical graphs and clustered graphs, Algorithmica, 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 w...

• Type: Journal
• Year: 2010
• Where: JDA
• Authors: Seok-Hee Hong, Hiroshi Nagamochi
• Keywords: Convex Polygon, Hierarchical Graphs, JDA 2010, Planar Graphs