Differential Flattening

Abstract

Amulti-layer graphconsists of multiple layers of weighted graphs, where the multiple layers represent the different aspects of relationships. Considering multiple aspects (i.e., layers) together is essential to achieve a comprehensive and consolidated view. In this article, we propose a novel framework ofdifferential flattening, which facilitates the analysis of multi-layer graphs, and apply this framework to community detection. Differential flattening merges multiple graphs into a single graph such that the graph structure with the maximum clustering coefficient is obtained from the single graph. It has two distinct features compared with existing approaches. First, dealing with multiple layers is doneindependentlyof a specific community detection algorithm, whereas previous approaches rely on a specific algorithm. Thus, any algorithm for a single graph becomes applicable to multi-layer graphs. Second, the contribution of each layer to the single graph is determinedautomaticallyfor the maximum clustering coefficient. Since differential flattening is formulated by an optimization problem, the optimal solution is easily obtained by well-known algorithms such as interior point methods. Extensive experiments were conducted using the Lancichinetti-Fortunato-Radicchi (LFR) benchmark networks as well as the DBLP, 20 Newsgroups, and MIT Reality Mining networks. The results show that our approach of differential flattening leads to discovery of higher-quality communities than baseline approaches and the state-of-the-art algorithms.