Fast Algorithm for Distance Dynamics-Based Community Detection

Abstract

Community detection is a fundamental problem in graph-based data analytics. Among many models, the distance dynamics model proposed recently is shown to be able to faithfully capture natural communities that are of different sizes. However, the state-of-the-art algorithm $\mathsf {Attractor}$ for distance dynamics does not scale to graphs with large maximum vertex degrees, which is the case for large real graphs. In this paper, we aim to scale distance dynamics to large graphs. To achieve that, we propose a fast distance dynamics algorithm $\mathsf {FDD}$. We show that $\mathsf {FDD}$ has a worst-case time complexity of $\mathcal{O}(T\cdot \gamma \cdot m)$, where T is the number of iterations until convergence, $\gamma$ is a small constant, and m is the number of edges in the input graph. Thus, the time complexity of $\mathsf {FDD}$ does not depend on the maximum vertex degree. Moreover, we also propose optimization techniques to alleviate the dependency on T. We conduct extensive empirical studies on large real graphs and demonstrate the efficiency and effectiveness of $\mathsf {FDD}$.