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A validity index approach for network partitions

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  • Liu, Jian
  • Li, Tiejun

Abstract

The validity index has been used to evaluate the fitness of partitions produced by clustering algorithms for points in Euclidean space. In this paper, we propose a new validity index for network partitions, which can provide a measure of goodness for the community structure of networks. It is defined as a product of two factors, and involves the compactness and separation for each partition. The simulated annealing strategy is used to minimize such a validity index function in coordination with our previous k-means algorithm based on the optimal reduction of a random walker Markovian dynamics on the network. It is demonstrated that the algorithm can efficiently find the community structure during the cooling process. The number of communities can be automatically determined without any prior knowledge of the community structure. Moreover, the algorithm is successfully applied to three real-world networks.

Suggested Citation

  • Liu, Jian & Li, Tiejun, 2011. "A validity index approach for network partitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3579-3591.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:20:p:3579-3591
    DOI: 10.1016/j.physa.2011.04.015
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    References listed on IDEAS

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    1. Barabási, A.L & Jeong, H & Néda, Z & Ravasz, E & Schubert, A & Vicsek, T, 2002. "Evolution of the social network of scientific collaborations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 590-614.
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    Cited by:

    1. van den Burg, S.W.K. & Bogaardt, M.J., 2014. "Business and biodiversity: A frame analysis," Ecosystem Services, Elsevier, vol. 8(C), pages 178-184.

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