Discovering the Densest Subgraph in MapReduce for Assortative Big Natural Graphs

Discovering the densest subgraph is important in graph analysis, which has wide-ranging applications from social network community mining to the discovery of biological network modules. However, the previous algorithms neglect the connectivity of the dense subgraph since it is a challenge to give consideration to both subgraph structure and time efficiency. As a result, it may lead to isolated subgraphs in the output though they aim to find one connected dense subgraph. Also, there are lacking of efficient algorithms for big natural graphs, especially considering datasets become increasingly larger in this era of Big Data. Furthermore, previous algorithms fail to take advantage of various features of natural graphs (e.g., power-law degree distribution, homophyly of vertices, and power-law community size) which can be applied to improve the efficiency and precision of the densest subgraph discovery. To handle these problems, we design a heuristic algorithm for discovering the connected densest subgraph for massive undirected graphs in a MapReduce framework by taking advantage of the features of natural graphs. Experimental results show that our algorithm is capable of discovering the connected densest subgraph. Also, it can reduce the running times by 62\% for average and discover denser subgraphs in 50\% of the real datasets and 88\% of the simulated datasets comparing with previous algorithm in a MapReduce framework.