Lossless Graph Summarization using Dense Subgraphs Discovery

Dense subgraph discovery, in a large graph, is useful to solve the community search problem. Motivated from this, we propose a graph summarization method where we search and aggregate dense subgraphs into super nodes. Since the dense subgraphs have high overlap of common neighbors, thus merging such subgraphs can produce a highly compact summary graph. Whereas the member nodes of each dense subgraph have many edges in common, they also have some edges not belonging to a given subgraph; which in turn reduce the compression ratio. To solve this problem, we propose the concept of AutoPruning that effectively filters the dense sub graphs having higher ratio of common to that of non-common neighbors. To summarize the dense subgraphs, we use the Minimum Description Length (MDL) principle to obtain a highly compact summary with least edge corrections for loss less compression. We propose two alternatives to trade-off the computation time and compression ratio while creating a super node from each dense subgraph. Through experiments on two publicly available real world graphs, we compare the proposed approach with the well known Minimum Degree Measure (MDM), for dense subgraph discovery, and observe very encouraging results.