Untangling the Hairballs of Multi-Centered, Small-World Online Social Media Networks

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, for instance, with graphs of high density or high conductance, or in the presence of high-degree vertices, all of which tend to pull vertices together and thus result in clutter overspreading variation in local density. We here propose a method specifically for a class of small-world graphs that are typical for online social networks. 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 criterion for structural 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 small-world graph prior to the application of a clustering algorithm. Submitted: November 2014 Reviewed: September 2015 Revised: September 2015 Accepted: September 2015 Final: September 2015 Published: November 2015 Article type: Regular paper Communicated by: C. Duncan and A. Symvonis This research was supported by DFG under grants GRK 1042, Br 2158/6-1, and Br 2158/11-1. The proposed method is available in visone. E-mail addresses: [email protected] (Arlind Nocaj) [email protected] (Mark Ortmann) [email protected] (Ulrik Brandes) 596 Nocaj, Ortmann, and Brandes Untangling Hairballs