IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v16y2025i1d10.1038_s41467-025-56034-2.html
   My bibliography  Save this article

Coarse-graining network flow through statistical physics and machine learning

Author

Listed:
  • Zhang Zhang

    (Beijing Normal University
    Swarma Research
    University of Padua)

  • Arsham Ghavasieh

    (Indiana University)

  • Jiang Zhang

    (Beijing Normal University
    Swarma Research)

  • Manlio Domenico

    (University of Padua
    University of Padua
    Sez.)

Abstract

Information dynamics plays a crucial role in complex systems, from cells to societies. Recent advances in statistical physics have made it possible to capture key network properties, such as flow diversity and signal speed, using entropy and free energy. However, large system sizes pose computational challenges. We use graph neural networks to identify suitable groups of components for coarse-graining a network and achieve a low computational complexity, suitable for practical application. Our approach preserves information flow even under significant compression, as shown through theoretical analysis and experiments on synthetic and empirical networks. We find that the model merges nodes with similar structural properties, suggesting they perform redundant roles in information transmission. This method enables low-complexity compression for extremely large networks, offering a multiscale perspective that preserves information flow in biological, social, and technological networks better than existing methods mostly focused on network structure.

Suggested Citation

  • Zhang Zhang & Arsham Ghavasieh & Jiang Zhang & Manlio Domenico, 2025. "Coarse-graining network flow through statistical physics and machine learning," Nature Communications, Nature, vol. 16(1), pages 1-11, December.
  • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-56034-2
    DOI: 10.1038/s41467-025-56034-2
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/s41467-025-56034-2
    File Function: Abstract
    Download Restriction: no

    File URL: https://libkey.io/10.1038/s41467-025-56034-2?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. Liao, Hao & Wu, Xingtong & Wang, Bing-Hong & Wu, Xiangyang & Zhou, Mingyang, 2019. "Solving the speed and accuracy of box-covering problem in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 954-963.
    2. Aaron Clauset & Cristopher Moore & M. E. J. Newman, 2008. "Hierarchical structure and the prediction of missing links in networks," Nature, Nature, vol. 453(7191), pages 98-101, May.
    3. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    4. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    5. Rui Ding & Norsidah Ujang & Hussain Bin Hamid & Mohd Shahrudin Abd Manan & Rong Li & Safwan Subhi Mousa Albadareen & Ashkan Nochian & Jianjun Wu, 2019. "Application of Complex Networks Theory in Urban Traffic Network Researches," Networks and Spatial Economics, Springer, vol. 19(4), pages 1281-1317, December.
    Full references (including those not matched with items on IDEAS)

    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. Leto Peel & Tiago P. Peixoto & Manlio De Domenico, 2022. "Statistical inference links data and theory in network science," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    2. Li, Heyang & Zeng, An, 2022. "Improving recommendation by connecting user behavior in temporal and topological dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    3. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    4. Guo, Fangjian & Yang, Zimo & Zhou, Tao, 2013. "Predicting link directions via a recursive subgraph-based ranking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3402-3408.
    5. Pavón-Domínguez, Pablo & Moreno-Pulido, Soledad, 2022. "Sandbox fixed-mass algorithm for multifractal unweighted complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    6. Huang, Liang & Zheng, Yu, 2023. "Asymptotic formula on APL of fractal evolving networks generated by Durer Pentagon," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    7. Peng Liu & Liang Gui & Huirong Wang & Muhammad Riaz, 2022. "A Two-Stage Deep-Learning Model for Link Prediction Based on Network Structure and Node Attributes," Sustainability, MDPI, vol. 14(23), pages 1-15, December.
    8. Lee, Yan-Li & Dong, Qiang & Zhou, Tao, 2021. "Link prediction via controlling the leading eigenvector," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    9. Ma, Fei & Wang, Ping, 2024. "Understanding influence of fractal generative manner on structural properties of tree networks," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    10. Miralles, Alicia & Comellas, Francesc & Chen, Lichao & Zhang, Zhongzhi, 2010. "Planar unclustered scale-free graphs as models for technological and biological networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1955-1964.
    11. Hu, Zhongren & Wu, Bo, 2023. "The average shortest distance of three colored substitution networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    12. Massimo Marchiori & Lino Possamai, 2015. "Micro-Macro Analysis of Complex Networks," PLOS ONE, Public Library of Science, vol. 10(1), pages 1-27, January.
    13. Samrachana Adhikari & Beau Dabbs, 2018. "Social Network Analysis in R: A Software Review," Journal of Educational and Behavioral Statistics, , vol. 43(2), pages 225-253, April.
    14. Wang, Xiaojie & Slamu, Wushour & Guo, Wenqiang & Wang, Sixiu & Ren, Yan, 2022. "A novel semi local measure of identifying influential nodes in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    15. Lin, Dan & Wu, Jiajing & Xuan, Qi & Tse, Chi K., 2022. "Ethereum transaction tracking: Inferring evolution of transaction networks via link prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    16. Ferreira, D.S.R. & Ribeiro, J. & Oliveira, P.S.L. & Pimenta, A.R. & Freitas, R.P. & Dutra, R.S. & Papa, A.R.R. & Mendes, J.F.F., 2022. "Spatiotemporal analysis of earthquake occurrence in synthetic and worldwide data," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    17. Qinghu Liao & Wenwen Dong & Boxin Zhao, 2023. "A New Strategy to Solve “the Tragedy of the Commons” in Sustainable Grassland Ecological Compensation: Experience from Inner Mongolia, China," Sustainability, MDPI, vol. 15(12), pages 1-24, June.
    18. Ding, Ying, 2011. "Community detection: Topological vs. topical," Journal of Informetrics, Elsevier, vol. 5(4), pages 498-514.
    19. Jianhong Chen & Hongcai Ma & Shan Yang, 2023. "SEIOR Rumor Propagation Model Considering Hesitating Mechanism and Different Rumor-Refuting Ways in Complex Networks," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    20. Pawanesh Pawanesh & Charu Sharma & Niteesh Sahni, 2025. "Analyzing Communicability and Connectivity in the Indian Stock Market During Crises," Papers 2502.08242, arXiv.org.

    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:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-56034-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.nature.com .

    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.