Skip to main content
SpringerLink
Log in

Missing nodes detection for complex networks based on graph convolutional networks

  • Original Research
  • Published:
Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

Network structure is an important and effective tool for describing things and the interrelationships between things and has been widely used in various research areas of complex networks, such as social networks, power networks, and biological networks. However, the observed networks are often incomplete and have missing nodes because of factors, such as data collection cost or permission. Missing nodes detection involves inferring whether there are missing nodes in the network and the location and neighborhood structure of the missing nodes based on the observed part of the complex networks. In this paper, a missing node detection algorithm based on graph convolutional networks is proposed. The algorithm divides the missing nodes detection task of the complex works into two subtasks: missing nodes existence detection and missing nodes structure inference. Specifically, we use graph convolutional networks to extract the nodes feature information and structure information, convert each node in the network into a low-dimensional latent representation, determine the existence of missing nodes by performing two consecutive layers of fully connected operations on latent variables, and perform linear operations on latent variables to infer the connection relationship between the missing nodes and other observable nodes. Then, we detect missing nodes in the complex network. We conduct experiments on real network datasets and artificially generated network datasets and find that the model can well solve the problem of detecting the missing nodes in complex networks and recovering the missing nodes and their connection structures with observable nodes of the networks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Acquisti A, Brandimarte L, Loewenstein G (2015) Privacy and human behavior in the age of information. Science 347(6221):509–514

    Article  Google Scholar 

  • Annibale A, Coolen ACC (2011) What you see is not what you get: how sampling affects macroscopic features of biological networks. Interface Focus 1(6):836–856

    Article  Google Scholar 

  • Aziz F, Gul H, Muhammad I, Uddin I (2020) Link prediction using node information on local paths. Physica A 557:124980

    Article  Google Scholar 

  • Benevenuto F, Rodrigues T, Cha M, Almeida V (2012) Characterizing user navigation and interactions in online social networks. Inf Sci 195:1–24

    Article  Google Scholar 

  • Bianchini M, Gori M, Scarselli F (2005) Inside pagerank. ACM Trans Internet Technol 5(1):92–128

    Article  Google Scholar 

  • Balas VE, Roy SS, Sharma D, Samui P (eds) (2019) Handbook of deep learning applications, vol 136. Springer, New York

    Google Scholar 

  • Clauset A, Moore C, Newman MEJ (2008) Hierarchical structure and the prediction of missing links in networks. Nature 453(7191):98–101

    Article  Google Scholar 

  • Cai L, Li J, Wang J, Ji S (2021) Line graph neural networks for link prediction. IEEE Trans Pattern Anal Mach Intell. doi: https://doi.org/10.1109/TPAMI.2021.3080635

    Article  Google Scholar 

  • Chen F, Pan S, Jiang J, Huo H, Long G (2019) DAGCN: dual attention graph convolutional networks. In: 2019 International Joint Conference on Neural Networks (IJCNN), 1–8

  • Dorogovtsev SN, Mendes JFF (2002) Evolution of networks. Adv Phys 51(4):1079–1187

    Article  Google Scholar 

  • Duan Y, Guan Q (2021) Predicting potential knowledge convergence of solar energy: bibliometric analysis based on link prediction model. Scientometrics 126(5):3749–3773

    Article  Google Scholar 

  • Eyal R, Kraus S, Rosenfeld A (2011) Identifying missing node information in social networks. In: Proceedings of the AAAI Conference on Artificial Intelligence, 25(1): 1166–1172

  • Fan J, Chow T (2017) Deep learning based matrix completion. Neurocomputing 266:540–549

    Article  Google Scholar 

  • Guimerà R, Sales-Pardo M (2009) Missing and spurious interactions and the reconstruction of complex networks. Proceedings of the National Academy of Sciences 106(52): 22073–22078

  • Getoor L, Friedman N, Koller D, Pfeffer A(2001) Learning probabilistic relational models. In:Relational Data Mining,307–335

  • Holland PW, Laskey KB, Leinhardt S (1983) Stochastic blockmodels: First steps. Social Networks 5(2):109–137

    Article  MathSciNet  Google Scholar 

  • Kim M, Leskovec J (2011) The network completion problem: inferring missing nodes and edges in networks. In: Proceedings of the 11th International Conference on Data Mining, 47–58

  • Kumar A, Singh SS, Singh K, Biswas B (2020) Link prediction techniques, applications, and performance: A survey. Physica A 553:124289

    Article  MathSciNet  MATH  Google Scholar 

  • Liben-Nowell D, Kleinberg J (2007) The link‐prediction problem for social networks. J Am Soc Inform Sci Technol 58(7):1019–1031

    Article  Google Scholar 

  • Lü L, Zhou T (2011) Link prediction in complex networks: A survey. Physica A 390(6):1150–1170

    Article  Google Scholar 

  • Lin TY, Goyal P, Girshick R, He K, Dollár P (2017) Focal loss for dense object detection. In: Proceedings of the IEEE international conference on computer vision, 2980–2988

  • Leskovec J, Chakrabarti D, Kleinberg J, Faloutsos C (2005) Realistic, mathematically tractable graph generation and evolution, using kronecker multiplication. In: European conference on principles of data mining and knowledge discovery. Springer, Berlin, Heidelberg, 133–145

  • Masrour F, Barjesteh I, Forsati R, Esfahanian AH, Radha H (2015) Network completion with node similarity: a matrix completion approach with provable guarantees. In: 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, 302–307

  • Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74(3):036104

    Article  MathSciNet  Google Scholar 

  • Niepert M, Ahmed M, Kutzkov K (2016) Learning convolutional neural networks for graphs. In: Proceedings of the 33th International Conference on Machine Learning, 2014–2023

  • Papagelis M, Das G, Koudas N (2011) Sampling online social networks. IEEE Trans Knowl Data Eng 25(3):662–676

    Article  Google Scholar 

  • Rossi A, Barbosa D, Firmani D, Matinata A, Merialdo P (2021) Knowledge graph embedding for link prediction: A comparative analysis. ACM Trans Knowl Discovery Data (TKDD) 15(2):1–49

    Article  Google Scholar 

  • Sina S, Rosenfeld A, Kraus S (2013) Solving the missing node problem using structure and attribute information. In: 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, 744–751

  • Spring N, Mahajan R, Wetherall D (2002) Measuring ISP topologies with rocketfuel. ACM SIGCOMM Computer Communication Review 32(4):133–145

    Article  Google Scholar 

  • Tylenda T, Angelova R, Bedathur S (2009) Towards time-aware link prediction in evolving social networks. In: Proceedings of the 3rd Workshop on Social Network Mining and Analysis, 1–10

  • Taskar B, Wong MF, Abbeel P, Koller D (2003) Link prediction in relational data. Adv Neural Inf Process Syst 16:659–666

    Google Scholar 

  • Theocharidis A, Van Dongen S, Enright AJ, Freeman TC (2009) Network visualization and analysis of gene expression data using Biolayout Express 3D. Nat Protoc 4(10):1535

    Article  Google Scholar 

  • Taguchi H, Liu X, Murata T (2021) Graph convolutional networks for graphs containing missing features. Future Generation Computer Systems 117:155–168

    Article  Google Scholar 

  • Wang L, Chen Q, Gao Z, Niu L, Zhao Y, Ma Z, Wu D (2015) Knowledge representation and general petri net models for power grid fault diagnosis. IET Generation, Transmission and Distribution 9(9): 866–873

  • Wei Q (2020) Network completion via deep metric learning. In: Journal of Physics: Conference Series, 1656(1): 012026

  • Yao L, Wang L, Pan L, Yao K (2016) Link prediction based on common-neighbors for dynamic social network. Procedia Comput Sci 83:82–89

    Article  Google Scholar 

  • Zhou T, Lü L, Zhang YC (2009) Predicting missing links via local information. Eur Phys J B 71(4):623–630

    Article  MATH  Google Scholar 

  • Zhang M, Chen Y (2017) Weisfeiler-Lehman neural machine for link prediction. In: Proceedings of the 23th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 575–583

  • Zhang M, Chen Y (2018) Link prediction based on graph neural networks. Adv Neural Inf Process Syst 31:5171–5181

    MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by Shanghai Philosophy and Social Science Planning Project (No.2021BTQ003), China Postdoctoral Science Foundation (2021M69235).

Author information

Authors and Affiliations

  1. Business School, University of Shanghai for Science and Technology, 20093, Shanghai, China

    Chen Liu, Ziran Li & Lixin Zhou

Authors
  1. Chen Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ziran Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lixin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lixin Zhou.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, C., Li, Z. & Zhou, L. Missing nodes detection for complex networks based on graph convolutional networks. J Ambient Intell Human Comput 14, 9145–9158 (2023). https://doi.org/10.1007/s12652-022-04418-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-022-04418-3

Keywords

Search

Navigation