Optimization of Graph Clustering Inspired by Dynamic Belief Systems

Graph clustering is essential to understand the nature and behavior of real world such as social network, technical network and transportation network. Different from the existing studies, we propose a new Markov clustering method inspired by belief dynamical system which can be used in general for optimization of different quality measures. By a rigorous theoretical proof, it has been shown that the quality function's global maximum is a dynamical system's asymptotically stable fixed point. Under specified conditions, the trajectory of the dynamical converges to the cluster labels of corresponding nodes. Particularly, a general formulation can unite well-known methodologies and the quality functions that correspond to them. The algorithm is fast and its computational complexity is nearly linear with the scale of sparse networks. Finally, we thoroughly evaluate our methodology on a variety of synthetic and real-world networks with various network properties, particularly on the dynamical networks. The results demonstrate that when compared to the current state-of-the-art algorithms, our method performs better on these networks.