Discovery of Top-k Dense Subgraphs in Dynamic Graph Collections

Dense subgraph discovery is a key issue in graph mining, due to its importance in several applications, such as correlation analysis, community discovery in the Web, gene co-expression and protein-protein interactions in bioinformatics. In this work, we study the discovery of the top-k dense subgraphs in a set of graphs. After the investigation of the problem in its static case, we extend the methodology to work with dynamic graph collections, where the graph collection changes over time. Our methodology is based on lower and upper bounds of the density, resulting in a reduction of the number of exact density computations. Our algorithms do not rely on user-defined threshold values and the only input required is the number of dense subgraphs in the result (k). In addition to the exact algorithms, an approximation algorithm is provided for top-k dense subgraph discovery, which trades result accuracy for speed. We show that a significant number of exact density computations is avoided, resulting in efficient monitoring of the top-k dense subgraphs.