IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v258y2017i3p844-865.html

Some searches may not work properly. We apologize for the inconvenience.

   My bibliography  Save this article

Efficient modularity density heuristics for large graphs

Author

Listed:
  • Santiago, Rafael
  • Lamb, Luís C.

Abstract

Modularity density maximization is a community detection optimization problem which improves the resolution limit degeneracy of modularity maximization. This paper presents seven scalable heuristics for modularity density and compares them with literature results from exact mixed integer linear programming and GAOD, iMeme-Net, HAIN, and BMD-λ heuristics. The results are also compared with CNM and Louvain, which are scalable heuristics for modularity maximization. The results suggest that our seven heuristics are faster than GAOD, iMeme-Net, HAIN, and BMD-λ modularity density heuristics. Our experiments also show that some of our heuristics surpassed the objective function value reported by iMeme-Net, Hain, and BMD-λ for some real graphs. Our seven heuristics were tested with real graphs from the Stanford Large Network Dataset Collection and the experiments show that they are scalable. This feature was confirmed by an amortized complexity analysis which reveals average linear time for three of our heuristics. Hypothesis tests suggest that four proposed heuristics are state-of-the-art since they are scalable for hundreds of thousands of nodes for the modularity density problem, and they find the high objective value partitions for the largest instances. Ground truth experiments in artificial random graphs were performed and suggest that our heuristics lead to better cluster detection than both CNM and Louvain.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:258:y:2017:i:3:p:844-865
    DOI: 10.1016/j.ejor.2016.10.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221716308670
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2016.10.033?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sun, Peng Gang, 2014. "Weighting links based on edge centrality for community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 346-357.
    2. Jiang, Jonathan Q. & McQuay, Lisa J., 2012. "Modularity functions maximization with nonnegative relaxation facilitates community detection in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 854-865.
    3. Costa, Alberto, 2015. "MILP formulations for the modularity density maximization problem," European Journal of Operational Research, Elsevier, vol. 245(1), pages 14-21.
    4. 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.
    5. G. Xu & S. Tsoka & L. G. Papageorgiou, 2007. "Finding community structures in complex networks using mixed integer optimisation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(2), pages 231-239, November.
    6. 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.
    7. Andrea Lancichinetti & Filippo Radicchi & José J Ramasco & Santo Fortunato, 2011. "Finding Statistically Significant Communities in Networks," PLOS ONE, Public Library of Science, vol. 6(4), pages 1-18, April.
    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. 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.
    2. Rosanna Grassi & Paolo Bartesaghi & Stefano Benati & Gian Paolo Clemente, 2021. "Multi-Attribute Community Detection in International Trade Network," Networks and Spatial Economics, Springer, vol. 21(3), pages 707-733, September.
    3. Baghersad, Milad & Emadikhiav, Mohsen & Huang, C. Derrick & Behara, Ravi S., 2023. "Modularity maximization to design contiguous policy zones for pandemic response," European Journal of Operational Research, Elsevier, vol. 304(1), pages 99-112.
    4. Van Nguyen, Truong & Zhang, Jie & Zhou, Li & Meng, Meng & He, Yong, 2020. "A data-driven optimization of large-scale dry port location using the hybrid approach of data mining and complex network theory," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).

    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. 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.
    2. Wu, Jianshe & Zhang, Long & Li, Yong & Jiao, Yang, 2016. "Partition signed social networks via clustering dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 568-582.
    3. Thang N. Dinh & Nam P. Nguyen & Md Abdul Alim & My T. Thai, 2015. "A near-optimal adaptive algorithm for maximizing modularity in dynamic scale-free networks," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 747-767, October.
    4. 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.
    5. 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.
    6. 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.
    7. Sun, Peng Gang, 2015. "Community detection by fuzzy clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 408-416.
    8. Harun Pirim & Burak Eksioglu & Fred W. Glover, 2018. "A Novel Mixed Integer Linear Programming Model for Clustering Relational Networks," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 492-508, February.
    9. Costa, Alberto, 2015. "MILP formulations for the modularity density maximization problem," European Journal of Operational Research, Elsevier, vol. 245(1), pages 14-21.
    10. 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.
    11. 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.
    12. Gregory, Steve, 2012. "Ordered community structure in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2752-2763.
    13. Ke Hu & Ju Xiang & Yun-Xia Yu & Liang Tang & Qin Xiang & Jian-Ming Li & Yong-Hong Tang & Yong-Jun Chen & Yan Zhang, 2020. "Significance-based multi-scale method for network community detection and its application in disease-gene prediction," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-24, March.
    14. de Arruda, Guilherme F. & Costa, Luciano da Fontoura & Rodrigues, Francisco A., 2012. "A complex networks approach for data clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6174-6183.
    15. Eustace, Justine & Wang, Xingyuan & Cui, Yaozu, 2015. "Overlapping community detection using neighborhood ratio matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 510-521.
    16. Kirsten Martinus & Thomas Sigler & Iacopo Iacopini & Ben Derudder, 2021. "The brokerage role of small states and territories in global corporate networks," Growth and Change, Wiley Blackwell, vol. 52(1), pages 12-28, March.
    17. 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.
    18. Ivan Blekanov & Svetlana S. Bodrunova & Askar Akhmetov, 2021. "Detection of Hidden Communities in Twitter Discussions of Varying Volumes," Future Internet, MDPI, vol. 13(11), pages 1-17, November.
    19. Fang, Wenyi & Wang, Xin & Liu, Longzhao & Wu, Zhaole & Tang, Shaoting & Zheng, Zhiming, 2022. "Community detection through vector-label propagation algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    20. Sho Tsugawa & Yukihiro Matsumoto & Hiroyuki Ohsaki, 2015. "On the robustness of centrality measures against link weight quantization in social networks," Computational and Mathematical Organization Theory, Springer, vol. 21(3), pages 318-339, September.

    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:eee:ejores:v:258:y:2017:i:3:p:844-865. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.