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

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, 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.

Adaptive Disentanglement Based on Local Clustering in Small-World Network Visualization

“…The most promising simplification approach for the discovery and visual exploration of cohesive sub-groups is to filter out edges based on an embeddedness criterion [7], [12], [13], [14], [15], which is determined based on the local density around an edge.…”

“…Consequently, identifying the optimal threshold, for which the group structure is most prominent in the layout, on a trial and error basis is a very time consuming task, particularly for large networks. [14] is extended by a process which analyzes all possible threshold parameters with respect to the group structure. This allows to point out interesting thresholds to the user as well as a fully automatic selection of this parameter.…”

“…2) An efficient dynamic algorithm maintaining the clustering coefficient under edge deletion, running in O(a(G)m) total time, where m is the number of edges in the graph and a (G) the arboricity -minimum number of spanning forests required to cover the edge set of a graph G. 3) An extensive evaluation of the effectiveness of our approach on a number of "real-world" as well as synthetic networks. To evaluate our preprocessing technique we use the quadrilateral Simmelian backbone, as the experimental study in [14] with various edge embeddedness metrics suggests that it is very well suited for untangling hairball graphs, while preserving the group structure. Especially for multi-centered small-world networks it enables standard force-directed layout techniques to strongly emphasize the inherent group structure in the final drawing.…”

“…We start by giving an overview of the backbone layout approach from [14) in the next section and explain our proposed quantification measure for the adaptive filtering in Section 3 . ln Section 4 we first evaluate how well this measure approximates the association with known clusters and then investigate its influence on the network layout.…”

Generative Data Models for Validation and Evaluation of Visualization Techniques

“…Sometimes local variation is introduced, and the distribution is pre-specified [117,80,9]. Such specifications may even be the result of users sketching adjacency matrices [124].…”