Planar Drawing of Clustered Graphs

Graphs are often used to represent relational information. As the amount of information that we want to visualize becomes larger and more complicated, classical graph model tends to be insuucient. In this paper, we introduce and show how to draw a practical and simple graph structure known as clustered graphs. We present an algorithm which produces planar, straight-line, convex drawings of clustered graphs in O(n 2:5) time. We also demonstrate an area lower bound and an angle upper bound for straight-line convex drawings of C-planar graphs. We show that such drawings require (2 n) area and the smallest angle is O(1=n). Our bounds are unlike the area and angle bounds of classical graph drawing conventions in which area bound is (n 2) and angle bounds are functions of the maximum degree of the graph. Our results indicate important tradeoos between line straightness and area, and between region convexity and area.