Linear Time Community Detection by a Novel Modularity Gain Acceleration in Label Propagation

Abstract

Community detection is an important problem in complex network analysis. Among numerous approaches for community detection, label propagation (LP) has attracted a lot of attention. LP selects the optimum community (i.e., label) of a network vertex by optimizing an objective function (e.g., Newman’s modularity) subject to the available labels in the vicinity of the vertex. In this article, a novel analysis of Newman’s modularity gain with respect to label transitions in graphs is presented. Here, we propose a new form of Newman’s modularity gain calculation that quantifies available label transitions for any LP based community detection. The proposed approach is called Modularity Gain Acceleration (MGA) and is simplified and divided into two components, the local and global sum-weights. The Local Sum-Weight (LSW) is the component with lower complexity and is calculated for each candidate label transition. The General Sum-Weight (GSW) is more computationally complex, and is calculated only once per each label. GSW is updated by leveraging a simple process for each node-label transition, instead of for all available labels. The proposed technique is applied to selected state-of-the-art LP-based community detection methods and the resulting network modularity and execution time are compared with traditional methods over small to big real world data sets. By applying MGA to LP-based methods, the run-time is significantly reduced–sometimes finishing before the traditional approach even finishes one iteration–achieving the same modularity performance and number of communities, i.e., community detection result. The MGA approach leads to significant efficiency improvements by reducing time consumption up to 85 percent relative to the original algorithms with the exact same quality in terms of modularity value which is highly valuable in analyses of big data sets.