## Drawing Clustered Graphs

 S. Hong and H. Nagamochi, "Convex Drawings of Hierarchical Planar Graphs and Clustered Planar Graphs", Journal of Discrete Algorithm, Elsevier, 8(3), pp. 282-295, 2010. In this paper, we present results on convex drawings of hierarchical graphs and clustered graphs. A convex drawing is a planar straight-line drawing of a plane graph, where every facial cycle is drawn as a convex polygon. Hierarchical graphs and clustered graphs are useful graph models with structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. We first present the necessary and sufficient conditions for a hierarchical plane graph to admit a convex drawing. More specifically, we show that the necessary and sufficient conditions for a biconnected plane graph due to Thomassen [C. Thomassen, Plane representations of graphs, in: J.A. Bondy, U.S.R. Murty (Eds.), Progress in Graph Theory, Academic Press, 1984, pp. 43-69] remains valid for the case of a hierarchical plane graph. We then prove that every internally triconnected clustered plane graph with a completely connected clustering structure admits a "fully convex drawing," a planar straight-line drawing such that both clusters and facial cycles are drawn as convex polygons. We also present algorithms to construct such convex drawings of hierarchical graphs and clustered graphs. Joshua Wing Kei Ho and Seok-Hee Hong, Drawing Clustered Graphs in Three Dimensions, Proceedings of Graph Drawing 2005, pp. 492-502, Lecture Notes in Computer Science 3843, 2005. Clustered graph is a very useful model for drawing large and complex networks. This paper presents a new method for drawing clustered graphs in three dimensions. The method uses a divide and conquer approach. More specifically, it draws each cluster in a 2D plane to minimise occlusion and ease navigation. Then a 3D drawing of the whole graph is constructed by combining these 2D drawings. Our main contribution is to develop three linear time weighted tree drawing algorithms in three dimensions for clustered graph layout. Further,we have implemented a series of six different layouts for clustered graphs by combining three 3D tree layouts and two 2D graph layouts. The experimental results with metabolic pathways show that our method can produce a nice drawing of a clustered graph which clearly shows visual separation of the clusters, as well as highlighting the relationships between the clusters. Sample drawings are available from http://www.cs.usyd.edu.au/visual/valacon/gallery/C3D/