Using graph partitioning to discover regions of correlated spatio-temporal change in evolving graphs

Abstract

There is growing interest in studying dynamic graphs, or graphs that evolve with time. In this work, we investigate a new type of dynamic graph analysis - finding regions of a graph that are evolving in a similar manner and are topologically similar over a period of time. For example, these regions can be used to group a set of changes having a common cause in event detection and fault diagnosis. Prior work [6] has proposed a greedy framework called cSTAG to find these regions. It was accurate in datasets where the regions are temporally and spatially well separated. However, in cases where the regions are not well separated, cSTAG produces incorrect groupings. In this paper, we propose a new algorithm called regHunter. It treats the region discovery problem as a multi-objective optimisation problem, and it uses a multi-level graph partitioning algorithm to discover the regions of correlated change. In addition, we propose an external clustering validation technique, and use several existing internal measures to evaluate the accuracy of regHunter. Using synthetic datasets, we found regHunter is significantly more accurate than cSTAG in dynamic graphs that have regions with small separation. Using two real datasets - the access graph of the 1998 World Cup website, and the BGP connectivity graph during the landfall of Hurricane Katrina - we found regHunter obtained more accurate results than cSTAG. Furthermore, regHunter was able to discover two interesting regions for the World Cup access graph that CSTAG was not able to find.