IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0147805.html
   My bibliography  Save this article

Z-Score-Based Modularity for Community Detection in Networks

Author

Listed:
  • Atsushi Miyauchi
  • Yasushi Kawase

Abstract

Identifying community structure in networks is an issue of particular interest in network science. The modularity introduced by Newman and Girvan is the most popular quality function for community detection in networks. In this study, we identify a problem in the concept of modularity and suggest a solution to overcome this problem. Specifically, we obtain a new quality function for community detection. We refer to the function as Z-modularity because it measures the Z-score of a given partition with respect to the fraction of the number of edges within communities. Our theoretical analysis shows that Z-modularity mitigates the resolution limit of the original modularity in certain cases. Computational experiments using both artificial networks and well-known real-world networks demonstrate the validity and reliability of the proposed quality function.

Suggested Citation

  • Atsushi Miyauchi & Yasushi Kawase, 2016. "Z-Score-Based Modularity for Community Detection in Networks," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-17, January.
    • Handle: RePEc:plo:pone00:0147805
    DOI: 10.1371/journal.pone.0147805
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0147805
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0147805&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0147805?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Martin Rosvall & Carl T Bergstrom, 2011. "Multilevel Compression of Random Walks on Networks Reveals Hierarchical Organization in Large Integrated Systems," PLOS ONE, Public Library of Science, vol. 6(4), pages 1-10, April.
    2. Sonia Cafieri & Alberto Costa & Pierre Hansen, 2014. "Reformulation of a model for hierarchical divisive graph modularity maximization," Annals of Operations Research, Springer, vol. 222(1), pages 213-226, November.
    3. Medus, A. & Acuña, G. & Dorso, C.O., 2005. "Detection of community structures in networks via global optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 358(2), pages 593-604.
    4. G. Agarwal & D. Kempe, 2008. "Modularity-maximizing graph communities via mathematical programming," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 66(3), pages 409-418, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jiajing Zhu & Yongguo Liu & Changhong Yang & Wen Yang & Zhi Chen & Yun Zhang & Shangming Yang & Xindong Wu, 2018. "A degree-based block model and a local expansion optimization algorithm for anti-community detection in networks," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-25, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiang, Ju & Tang, Yan-Ni & Gao, Yuan-Yuan & Zhang, Yan & Deng, Ke & Xu, Xiao-Ke & Hu, Ke, 2015. "Multi-resolution community detection based on generalized self-loop rescaling strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 127-139.
    2. Liu, X. & Murata, T., 2010. "Advanced modularity-specialized label propagation algorithm for detecting communities in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1493-1500.
    3. Dušan Džamić & Daniel Aloise & Nenad Mladenović, 2019. "Ascent–descent variable neighborhood decomposition search for community detection by modularity maximization," Annals of Operations Research, Springer, vol. 272(1), pages 273-287, January.
    4. Sukeda, Issey & Miyauchi, Atsushi & Takeda, Akiko, 2023. "A study on modularity density maximization: Column generation acceleration and computational complexity analysis," European Journal of Operational Research, Elsevier, vol. 309(2), pages 516-528.
    5. Li, Zhangtao & Liu, Jing, 2016. "A multi-agent genetic algorithm for community detection in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 336-347.
    6. Santiago, Rafael & Lamb, Luís C., 2017. "Efficient modularity density heuristics for large graphs," European Journal of Operational Research, Elsevier, vol. 258(3), pages 844-865.
    7. Chakraborty, Abhijit & Krichene, Hazem & Inoue, Hiroyasu & Fujiwara, Yoshi, 2019. "Characterization of the community structure in a large-scale production network in Japan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 210-221.
    8. Rosa Rodriguez-Sánchez & J. A. García & J. Fdez-Valdivia, 2014. "Evolutionary games between subject categories," Scientometrics, Springer;Akadémiai Kiadó, vol. 101(1), pages 869-888, October.
    9. Michele Coscia & Ricardo Hausmann, 2015. "Evidence That Calls-Based and Mobility Networks Are Isomorphic," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-15, December.
    10. Daisuke Sato & Yuichi Ikeda & Shuichi Kawai & Maxmilian Schich, 2020. "The sustainability and the survivability of Kyoto’s traditional craft industry revealed from supplier-customer network," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-23, November.
    11. Amulyashree Sridhar & Sharvani GS & AH Manjunatha Reddy & Biplab Bhattacharjee & Kalyan Nagaraj, 2019. "The Eminence of Co-Expressed Ties in Schizophrenia Network Communities," Data, MDPI, vol. 4(4), pages 1-23, November.
    12. Ponce, Diego & Puerto, Justo & Temprano, Francisco, 2024. "Mixed-integer linear programming formulations and column generation algorithms for the Minimum Normalized Cuts problem on networks," European Journal of Operational Research, Elsevier, vol. 316(2), pages 519-538.
    13. Hiromitsu Goto & Wataru Souma & Mari Jibu & Yuichi Ikeda, 2020. "Multilayer Network Analysis of the Drug Pipeline in the Global Pharmaceutical Industry," Papers 2003.04620, arXiv.org.
    14. Alessandro Tavoni & Simon Levin, 2014. "Managing the climate commons at the nexus of ecology, behaviour and economics," Nature Climate Change, Nature, vol. 4(12), pages 1057-1063, December.
    15. Bech, Morten L. & Bergstrom, Carl T. & Rosvall, Martin & Garratt, Rodney J., 2015. "Mapping change in the overnight money market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 44-51.
    16. Yian Yin & Yuxiao Dong & Kuansan Wang & Dashun Wang & Benjamin F. Jones, 2022. "Public use and public funding of science," Nature Human Behaviour, Nature, vol. 6(10), pages 1344-1350, October.
    17. Abhijit Chakraborty & Yuichi Kichikawa & Takashi Iino & Hiroshi Iyetomi & Hiroyasu Inoue & Yoshi Fujiwara & Hideaki Aoyama, 2018. "Hierarchical communities in the walnut structure of the Japanese production network," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-25, August.
    18. Vincent Labatut & Jean-Michel Balasque, 2012. "Detection and Interpretation of Communities in Complex Networks: Methods and Practical Application," Post-Print hal-00633653, HAL.
    19. Yazdanparast, Sakineh & Havens, Timothy C., 2017. "Modularity maximization using completely positive programming," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 20-32.
    20. Dong Wang & Jiexun Li & Kaiquan Xu & Yizhen Wu, 2017. "Sentiment community detection: exploring sentiments and relationships in social networks," Electronic Commerce Research, Springer, vol. 17(1), pages 103-132, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0147805. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.