A comparison of vertex ordering algorithms for large graph visualization

Abstract

In this study, we examine the use of graph ordering algorithms for visual analysis of data sets using visual similarity matrices. Visual similarity matrices display the relationships between data items in a dot-matrix plot format, with the axes labeled with the data items and points drawn if there is a relationship between two data items. The biggest challenge for displaying data using this representation is finding an ordering of the data items that reveals the internal structure of the data set. Poor orderings are indistinguishable from noise whereas a good ordering can reveal complex and subtle features of the data. We consider three general classes of algorithms for generating orderings: simple graph theoretic algorithms, symbolic sparse matrix reordering algorithms, and spectral decomposition algorithms. We apply each algorithm to synthetic and real world data sets and evaluate each algorithm for interpretability (i.e., does the algorithm lead to images with usable visual features?) and stability (i.e., does the algorithm consistently produce similar results?). We also provide a detailed discussion of the results for each algorithm across the different graph types and include a discussion of some strategies for using ordering algorithms for data analysis based on these results.