- Published 2012 in Graph Drawing

Large graphs appear in many application domains. Their analysis can be done automatically by machines, for which the graph size is less of a problem, or, especially for exploration tasks, visually by humans. The graph drawing literature contains many efficient methods for visualizing large graphs, see e.g. [4, Chapter 12], but for large graphs it is often useful to first compute a sequence of coarser and more abstract representations by grouping vertices recursively using a hierarchical clustering algorithm. Then the task is to compute an overview picture of the graph based on a given cluster hierarchy, such that details of the graph, e.g., within clusters, remain visible on demand. This problem has been studied before. For example, Bourqui et al. [1] presented a method to draw hierarchically clustered graphs in a top-down fashion using Voronoi cells as cluster regions and a force-directed algorithm to draw each cluster. They did not explicitly consider inter-cluster forces between different levels of the hierarchy. Didimo and Montecchiani [2] recently presented a fast space-filling force-directed algorithm to compute 2D layouts of large hierarchically clustered graphs, where cluster regions are rectangles obtained from a treemap layout. The contribution of our work is the design and implementation of a 2D layout algorithm for hierarchically clustered graphs that is specifically tailored for lifting the vertices to the surface of a 3D landscape in order to visualize various features of the graph such as average vertex degree and cluster density; such visualizations are known as landscape metaphors [3]. Our algorithm runs in two phases. The first step computes a force-directed 2D layout with circular cluster regions that is tailored to the subsequent lifting step using a Gaussian filter that matches the circular cluster shapes.

@inproceedings{Athenstdt2012VisualizingLH,
title={Visualizing Large Hierarchically Clustered Graphs with a Landscape Metaphor},
author={Jan Christoph Athenst{\"a}dt and Robert G{\"{o}rke and Marcus Krug and Martin N{\"{o}llenburg},
booktitle={Graph Drawing},
year={2012}
}