Untangling hairballs : From 3 to 14 degrees of separation

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CHRISTIAN DUNCAN ..., , ed.. Graph Drawing : 22nd International Symposium, GD 2014, Würzburg, Germany, September 24-26, 2014 ; revised selected papers. Berlin [u.a.]: Springe, 2014, pp. 101-112. Lecture Notes in Computer Science. 8871. ISBN 978-3-662-45802-0. Available under: doi: 10.1007/978-3-662-45803-7_9
Zusammenfassung

Small-world graphs have characteristically low average distance and thus cause force-directed methods to generate drawings that look like hairballs. This is by design as the inherent objective of these methods is a globally uniform edge length or, more generally, accurate distance representation. The problem arises in graphs of high density or high conductance, and in the presence of high-degree vertices, all of which tend to pull vertices together and thus clutter variation in local density.

We here propose a method to draw online social networks, a special class of hairball graphs. The method is based on a spanning subgraph that is sparse but connected and consists of strong ties holding together communities. To identify these ties we propose a novel measure of embeddedness. It is based on a weighted accumulation of triangles in quadrangles and can be determined efficiently. An evaluation on empirical and generated networks indicates that our approach improves upon previous methods using other edge indices. Although primarily designed to achieve more informative drawings, our spanning subgraph may also serve as a sparsifier that trims a hairball graph before the application of a clustering algorithm.

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22nd International Symposium, Graph Drawing 2014, 24. Sept. 2014 - 26. Sept. 2014, Würzburg
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ISO 690NOCAJ, Arlind, Mark ORTMANN, Ulrik BRANDES, 2014. Untangling hairballs : From 3 to 14 degrees of separation. 22nd International Symposium, Graph Drawing 2014. Würzburg, 24. Sept. 2014 - 26. Sept. 2014. In: CHRISTIAN DUNCAN ..., , ed.. Graph Drawing : 22nd International Symposium, GD 2014, Würzburg, Germany, September 24-26, 2014 ; revised selected papers. Berlin [u.a.]: Springe, 2014, pp. 101-112. Lecture Notes in Computer Science. 8871. ISBN 978-3-662-45802-0. Available under: doi: 10.1007/978-3-662-45803-7_9
BibTex
@inproceedings{Nocaj2014Untan-30583,
  year={2014},
  doi={10.1007/978-3-662-45803-7_9},
  title={Untangling hairballs : From 3 to 14 degrees of separation},
  number={8871},
  isbn={978-3-662-45802-0},
  publisher={Springe},
  address={Berlin [u.a.]},
  series={Lecture Notes in Computer Science},
  booktitle={Graph Drawing : 22nd International Symposium, GD 2014, Würzburg, Germany, September 24-26, 2014 ; revised selected papers},
  pages={101--112},
  editor={Christian Duncan ...},
  author={Nocaj, Arlind and Ortmann, Mark and Brandes, Ulrik}
}
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