How to draw a planar clustered graph

Abstract

In this paper, we introduce and show how to draw a practical 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 Ω(2ⁿ) 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 Ω(n²) and angle bounds are functions of the maximum degree of the graph. Our results indicate important tradeoff between line straightness and area, and between region convexity and area.