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A spectral method to find communities in bipartite networks

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  • Feng, Liang
  • Zhou, Cangqi
  • Zhao, Qianchuan

Abstract

Community detection in complex networks that aims to find partitions of networks with dense intra-edges and sparse inter-edges, has recently attracted lots of interest in many fields. Specially, bipartite networks composed of two different types of vertices are the common representations for many real-world networks, such as actor–film, consumer–product networks, etc. In this paper, we show that optimizing Barber’s bipartite modularity, which is widely used to evaluate partitions of bipartite networks, can be reformulated as a spectral problem with appropriate relaxations. We further propose a new method combining singular value decomposition(SVD) and BRIM algorithm to obtain an optimal community partition. Compared with many other algorithms, the new method can give us a more detailed and comprehensive view of the original bipartite network for different cluster numbers k. We test our method on both synthetic networks and two benchmark data sets. Experimental results show that, our method is not only capable to extract a community partition with a larger bipartite modularity, but also converge to the exact underlying community partition when k is appropriately set, which helps to alleviate the resolution limit issue to some extent.

Suggested Citation

  • Feng, Liang & Zhou, Cangqi & Zhao, Qianchuan, 2019. "A spectral method to find communities in bipartite networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 424-437.
  • Handle: RePEc:eee:phsmap:v:513:y:2019:i:c:p:424-437
    DOI: 10.1016/j.physa.2018.09.022
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    References listed on IDEAS

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    1. Shang, Jiaxing & Liu, Lianchen & Li, Xin & Xie, Feng & Wu, Cheng, 2016. "Targeted revision: A learning-based approach for incremental community detection in dynamic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 70-85.
    2. Mukherjee, Animesh & Choudhury, Monojit & Ganguly, Niloy, 2011. "Understanding how both the partitions of a bipartite network affect its one-mode projection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3602-3607.
    3. Rizman Žalik, Krista & Žalik, Borut, 2014. "A local multiresolution algorithm for detecting communities of unbalanced structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 380-393.
    4. Heimo, Tapio & Tibély, Gergely & Saramäki, Jari & Kaski, Kimmo & Kertész, János, 2008. "Spectral methods and cluster structure in correlation-based networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5930-5945.
    5. Zhou, Cangqi & Feng, Liang & Zhao, Qianchuan, 2018. "A novel community detection method in bipartite networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1679-1693.
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    Cited by:

    1. Fan, Xinyan & Fang, Kuangnan & Pu, Dan & Qin, Ruixuan, 2024. "Generalized latent space model for one-mode networks with awareness of two-mode networks," Computational Statistics & Data Analysis, Elsevier, vol. 193(C).
    2. Yubo Peng & Bofeng Zhang & Furong Chang, 2021. "Overlapping Community Detection of Bipartite Networks Based on a Novel Community Density," Future Internet, MDPI, vol. 13(4), pages 1-21, March.
    3. Wu, Yujia & Lan, Wei & Fan, Xinyan & Fang, Kuangnan, 2024. "Bipartite network influence analysis of a two-mode network," Journal of Econometrics, Elsevier, vol. 239(2).
    4. Huang, Danyang & Wang, Feifei & Zhu, Xuening & Wang, Hansheng, 2020. "Two-mode network autoregressive model for large-scale networks," Journal of Econometrics, Elsevier, vol. 216(1), pages 203-219.

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