SCIENTIA SINICA Mathematica, Volume 47 , Issue 2 : 241-256(2017) https://doi.org/10.1360/N012015-00284

A linear community detection algorithm based on dynamical\\ system in networks

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  • ReceivedSep 6, 2015
  • AcceptedFeb 17, 2016
  • PublishedAug 8, 2016


Detection of communities or clustering is particularly valuable for understanding, analyzing and optimizing many natural and engineering complex networks, such as gene regulatory networks, smart grid and transportation networks. Present techniques relies heavily on the optimization or heuristic methods, which cannot balance the computational efficiency and accuracy. In this paper, we propose an iterative algorithm to realize the exact detection of network communities, by using a novel method based on dynamical system. We first introduce a discrete-time dynamical system that characterizes the evolutionary iteration of community membership from a random configure to the optimal one, and then specify the conditions that can direct the trajectory of this dynamical system to the convergence, which reveals the community label of each node. The computational complexity analysis shows the high-performance of our algorithm: The required computational time is linearly dependent on the total number of nodes in a sparse network. Analyzing the eigenvalue gap of the Markovian transition matrix, a rigorous theory is provided to find the optimal number of communities divided from a network. We also show that the new algorithm can be generalized to unify the conventional algorithms that are widely used. Finally, we perform extensive simulations using both synthetic and real-world benchmark networks to illustrate the nice performance of our method.

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