Untangling Hairballs

Abstract

Abstract. 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.

Mediatized Taiwanese Mandarin: A Text-mining Approach to Speaker Stereotypes

“…The more comments they co-occur in, the stronger the link is. After trial and error, the top 150 links were selected for interpretability of the network visualization and to prevent the graph from turning into a "hairball" (Nocaj et al 2014), which is not helpful for interpretation. For the network visualization, different clusters in the network were color coded to indicate the distinct "themes" of the online discourse.…”

GraphMaps: Browsing Large Graphs as Interactive Maps

“…Visualizing and evaluating clusterings. The test graph of our first experiment is the Caltech graph, which was used by Nocaj et al [17]. It is the graph of Facebook friend-ships at California Institute of Technology from September 2005 and contains 769 nodes and 16k edges [21].…”

Persistent Homology Guided Force-Directed Graph Layouts

“…The graph has 762 nodes and 16, 651 edges. For this example, we compare against modularity hierarchical clustering and adaptive refinement techniques [70,71]. Each of the techniques presents similar looking communities.…”

“…(a) Adaptive Refinement from[71] (b) Adaptive Refinement from[70] (c) Modularity Hierarchical Clustering (d) Our Approach Caltech datasets containing 762 nodes and 16, 651 edges are compared using (a,b) 2 adaptive refinement techniques, (c) modularity hierarchical clustering, and (d) our approach.…”