On compressing weighted time-evolving graphs

Existing graph compression techniquesmostly focus on static graphs. However for many practical graphs such as social networks the edge weights frequently change over time. This phenomenon raises the question of how to compress dynamic graphs while maintaining most of their intrinsic structural patterns at each time snapshot. In this paper we show that the encoding cost of a dynamic graph is proportional to the heterogeneity of a three dimensional tensor that represents the dynamic graph. We propose an effective algorithm that compresses a dynamic graph by reducing the heterogeneity of its tensor representation, and at the same time also maintains a maximum lossy compression error at any time stamp of the dynamic graph. The bounded compression error benefits compressed graphs in that they retain good approximations of the original edge weights, and hence properties of the original graph (such as shortest paths) are well preserved. To the best of our knowledge, this is the first work that compresses weighted dynamic graphs with bounded lossy compression error at any time snapshot of the graph.