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Abstract: Community structure analysis is a powerful tool for complex networks, whichcan simplify their functional analysis considerably. Recently, many approacheswere proposed to community structure detection, but few works were focused onthe significance of community structure. Since real networks obtained fromcomplex systems always contain error links, and most of the community detectionalgorithms have random factors, evaluate the significance of communitystructure is important and urgent. In this paper, we use the eigenvectors-stability to characterize the significance of community structures. Byemploying the eigenvalues of Laplacian matrix of a given network, we canevaluate the significance of its community structure and obtain the optimalnumber of communities, which are always hard for community detectionalgorithms. We apply our method to many real networks. We find that significantcommunity structures exist in many social networks and C.elegans neuralnetwork, and that less significant community structures appear inprotein-interaction networks and metabolic networks. Our method can be appliedto broad clustering problems in data mining due to its solid mathematical basisand efficiency.



Author: Yanqing Hu, Yiming Ding, Ying Fan, Zengru Di

Source: https://arxiv.org/



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