Target Netgrams: An Annulus-constrained Stress Model for
Radial Graph Visualization

Mingliang Xue1     Yunhai Wang1     Chang Han1     Jian Zhang2    
Zheng Wang3     Kaiyi Zhang1     Christophe Hurter4     Jian Zhao5     Oliver Deussen6

1Shandong University    
2Computer Network Information Center, Chinese Academy of Sciences    
3China information consulting & designing institute    
4Ecole National de l’Aviation Civile, Toulouse, France.    
5Cheriton School of Computer Science, University of Waterloo    
6Computer and Information Science, University of Konstanz

Accepted by IEEE Transactions on Visualization and Computer Graphics

Fig. 1. Visualization of a graph of researchers selected from co-authorships in Network Science using different layout methods: (a) traditional radial layout (TR), (b) more flexible radial layout (FR), and (c) our Target Netgram, (TN). TR fails to show the clusters (green and orange nodes) and results in heavy visual clutter (blue nodes), while FR does preserve these two clusters to some extent but induces heavy node overlap so that the relationship between nodes cannot be clearly discerned. In contrast, our method is able to show cluster structures as well as accurately place nodes into the corresponding annuli.


We present Target Netgrams as a visualization technique for radial layouts of graphs. Inspired by manually created target sociograms, we propose an annulus-constrained stress model that aims to position nodes onto the annuli between adjacent circles for indicating their radial hierarchy, while maintaining the network structure (clusters and neighborhoods) and improving readability as much as possible. This is achieved by having more space on the annuli than traditional layout techniques. By adapting stress majorization to this model, the layout is computed as a constrained least square optimization problem. Additional constraints (e.g., parent-child preservation, attribute-based clusters and structure-aware radii) are provided for exploring nodes, edges, and levels of interest. We demonstrate the effectiveness of our method through a comprehensive evaluation, a user study, and a case study.



Paper (12.3M)



Figure 13. Interactive exploration of a collaboration network extracted from the DBLP dataset. (a) Initial layout generated by \metaphor. (b) A user zooms into the first annulus and adds pie charts on the corresponding nodes. (c) Layout after the user applied the constraint of attribute-based cluster.


The authors like to thank the anonymous reviewers for their valuable input. This work was supported by the grants of the National Key Research & Development Plan of China (2019YFB1704201), and NSFC (62132017, 62141217).