DSS: Drawing Dynamic Graphs with Spectral Sparsification

Abstract

This paper presents DSS (Dynamic Spectral Sparsification), a sampling approach for drawing large and complex dynamic graphs which can preserve important structural properties of the original graph. Specifically, we present two variants: DSSI (Independent) which performs spectral sparsification independently on each dynamic graph time slice; and DSS-U (Union) which performs spectral sparsification on the union graph of all time slices. Moreover, for evaluation of dynamic graph drawing using sampling approach, we introduce two new metrics: DSQ (Dynamic Sampling Quality) to measure how faithfully the samples represent the ground truth change in the dynamic graph, and DSDQ (Dynamic Sampling Drawing Quality) to measure how faithfully the drawings of the sample represent the ground truth change. Experiments demonstrate that DSS significantly outperform random sampling on quality metrics and visual comparison. On average, DSS obtains over 80% (resp., 30%) better DSQ (resp., DSDQ) than random sampling, and visually better preserves the ground truth changes in dynamic graphs.