Stuart Golodetz, Anurag Arnab, Irina Voiculescu and Stephen Cameron

🏢 Pattern Recognition, July 2020

**Abstract.** Graphs are an invaluable modelling tool in many domains, but visualising large graphs in their entirety can be difficult. Hierarchical graph visualisation - recursively clustering a graph's nodes to view it at a higher level of abstraction - has thus become popular. However, this can hide important information that a user needs to understand a graph's topology, e.g. nodes' neighbourhoods. TugGraph addressed this by "separating out" a given node's neighbours from their hierarchy ancestors to visualise them independently. Its original implementation was straightforward, but copied parts of the hierarchy, making it slow and memory-hungry. An optimised later version, which we refer to as FastTug, avoided this, but at a cost in clarity. Optimising TugGraph without sacrificing clarity is difficult because of the need to keep every hierarchy node connected, a common challenge for graph hierarchy editing algorithms. Recently, this problem has been addressed by "zipping" algorithms, multi-level split/merge algorithms that preserve hierarchy node connectedness and can be built upon for higher-level editing. In this paper, we generalise the original unzipping algorithms to implement SimpleTug, a simple, modular version of TugGraph that is easy to understand and implement, and even faster and more memory-efficient than FastTug. We formally prove its equivalence to FastTug, and show how both can be parallelised. Using our millipede hierarchical image segmentation system, we show experimentally that both the serial and parallel versions of SimpleTug are around 25% faster than their FastTug counterparts, whilst using considerably less memory. Finally, we discuss the interesting theoretical connections between TugGraph and zipping, and suggest ideas for further work.