Skip to main content
SpringerLink
Log in

Ranking influential nodes in complex networks based on local and global structures

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Identifying influential nodes in complex networks is an open and challenging issue. Many measures have been proposed to evaluate the influence of nodes and improve the accuracy of measuring influential nodes. In this paper, a new method is proposed to identify and rank the influential nodes in complex networks. The proposed method determines the influence of a node based on its local location and global location. It considers both the local and global structure of the network. Traditional degree centrality is improved and combined with the notion of the local clustering coefficient to measure the local influence of nodes, and the classical k-shell decomposition method is improved to measure the global influence of nodes. To evaluate the performance of the proposed method, the susceptible-infected-recovered (SIR) model is utilized to examine the spreading capability of nodes. A number of experiments are conducted on 11 real-world networks to compare the proposed method with other methods. The experimental results show that the proposed method can identify the influential nodes more accurately than other methods.

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

Similar content being viewed by others

Data availability

Not applicable.

References

  1. Lü L, Chen D, Ren X-L, Zhang Q-M, Zhang Y-C, Zhou T (2016) Vital nodes identification in complex networks. PhR 650:1–63. https://doi.org/10.1016/j.physrep.2016.06.007

    Article  MathSciNet  Google Scholar 

  2. Fei L, Mo H, Deng Y (2017) A new method to identify influential nodes based on combining of existing centrality measures. MPLB 31(26):1750243. https://doi.org/10.1142/s0217984917502438

    Article  Google Scholar 

  3. Wang S, Du Y, Deng Y (2017) A new measure of identifying influential nodes: efficiency centrality. Commun Nonlinear Sci Numer Simul 47:151–163. https://doi.org/10.1016/j.cnsns.2016.11.008

    Article  MathSciNet  MATH  Google Scholar 

  4. Wang Z, Andrews MA, Wu Z-X, Wang L, Bauch CT (2015) Coupled disease–behavior dynamics on complex networks: a review. PhLRv 15:1–29. https://doi.org/10.1016/j.plrev.2015.07.006

    Article  Google Scholar 

  5. Li H-J, Zhang X-S (2013) Analysis of stability of community structure across multiple hierarchical levels. EPL (Europhysics Letters) 103(5):58002. https://doi.org/10.1209/0295-5075/103/58002

    Article  Google Scholar 

  6. Malliaros FD, Rossi M-EG, Vazirgiannis M (2016) Locating influential nodes in complex networks. Sci Rep 6:19307

    Article  Google Scholar 

  7. Gao L, Wang W, Shu P, Gao H, Braunstein LA (2017) Promoting information spreading by using contact memory. Epl 118(1):18001. https://doi.org/10.1209/0295-5075/118/18001

    Article  Google Scholar 

  8. Sheikhahmadi A, Nematbakhsh MA (2017) Identification of multi-spreader users in social networks for viral marketing. J Inf Sci 43(3):412–423

    Article  Google Scholar 

  9. Zamora-López G, Zhou C, Kurths J (2010) Cortical hubs form a module for multisensory integration on top of the hierarchy of cortical networks. Front Neuroinform 4:1. https://doi.org/10.3389/neuro.11.001.2010

    Article  Google Scholar 

  10. Zhang X, Zhu J, Wang Q, Zhao H (2013) Identifying influential nodes in complex networks with community structure. Knowl-Based Syst 42:74–84. https://doi.org/10.1016/j.knosys.2013.01.017

    Article  Google Scholar 

  11. Cho Y, Hwang J, Lee D (2012) Identification of effective opinion leaders in the diffusion of technological innovation: a social network approach. Technol Forecast Soc Change 79(1):97–106. https://doi.org/10.1016/j.techfore.2011.06.003

    Article  Google Scholar 

  12. Li H-R, Chen T-C, Hsiao C-L, Shi L, Chou C-Y, J-r H (2018) The physical forces mediating self-association and phase-separation in the C-terminal domain of TDP-43. Biochim Biophys Acta 1866(2):214–223. https://doi.org/10.1016/j.bbapap.2017.10.001

    Article  Google Scholar 

  13. Sheng J, Dai J, Wang B, Duan G, Long J, Zhang J, Guan K, Hu S, Chen L, Guan W (2020) Identifying influential nodes in complex networks based on global and local structure. Physica A: Stat Mech its Appl 541:123262. https://doi.org/10.1016/j.physa.2019.123262

    Article  Google Scholar 

  14. Freeman LC (1978) Centrality in social networks conceptual clarification. Social Netwks 1(3):215–239. https://doi.org/10.1016/0378-8733(78)90021-7

    Article  Google Scholar 

  15. Newman MEJ (2005) A measure of betweenness centrality based on random walks. Social Netwks 27(1):39–54. https://doi.org/10.1016/j.socnet.2004.11.009

    Article  Google Scholar 

  16. Sabidussi G (1966) The centrality index of a graph. Psychometrika 31(4):581–603

    Article  MathSciNet  Google Scholar 

  17. Opsahl T, Agneessens F, Skvoretz J (2010) Node centrality in weighted networks: generalizing degree and shortest paths. Social Netwks 32(3):245–251. https://doi.org/10.1016/j.socnet.2010.03.006

    Article  Google Scholar 

  18. Kitsak M, Gallos LK, Havlin S, Liljeros F, Muchnik L, Stanley HE, Makse HA (2010) Identification of influential spreaders in complex networks. NatPh 6(11):888–893. https://doi.org/10.1038/nphys1746

    Article  Google Scholar 

  19. Pastor-Satorras R, Vespignani A (2001) Epidemic spreading in scale-free networks. PhRvL 86(14):3200–3203

    Google Scholar 

  20. Newman MEJ (2002) Spread of epidemic disease on networks. Phys Rev E Stat Nonlinear Soft Matter Physics 66(1 Pt 2):016128

    Article  MathSciNet  Google Scholar 

  21. Albert R, Jeong H, Barabási A-L (2000) Error and attack tolerance of complex networks. Natur 406(6794):378–382

    Article  Google Scholar 

  22. Shimbel A (1953) Structural parameters of communication networks. Bull Math Biophys 15(4):501–507. https://doi.org/10.1007/BF02476438

    Article  MathSciNet  Google Scholar 

  23. Lü L, Zhou T, Zhang Q-M, Stanley HE (2016) The H-index of a network node and its relation to degree and coreness. Nat Commun 7:10168

    Article  Google Scholar 

  24. Liu Q, Zhu Y-X, Jia Y, Deng L, Zhou B, Zhu J-X, Zou P (2018) Leveraging local h-index to identify and rank influential spreaders in networks. Physica A: Stat Mech its Appl 512:379–391. https://doi.org/10.1016/j.physa.2018.08.053

    Article  Google Scholar 

  25. Zareie A, Sheikhahmadi A (2019) EHC: extended H-index centrality measure for identification of users’ spreading influence in complex networks. Physica A: Statist Mech its Appl 514:141–155. https://doi.org/10.1016/j.physa.2018.09.064

    Article  Google Scholar 

  26. Zareie A, Sheikhahmadi A, Fatemi A (2017) Influential nodes ranking in complex networks: an entropy-based approach. Chaos, Solitons Fractals 104:485–494

    Article  Google Scholar 

  27. Zeng A, Zhang CJ (2013) Ranking spreaders by decomposing complex networks. PhLA 377(14):1031–1035

    Google Scholar 

  28. Bae J, Kim S (2014) Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Physica a-Stat Mech Its Appl 395:549–559

    Article  MathSciNet  Google Scholar 

  29. Wang ZX, Zhao Y, Xi JK, Du CJ (2016) Fast ranking influential nodes in complex networks using a k-shell iteration factor. Physica a-Statist Mech Its Appl 461:171–181

    Article  Google Scholar 

  30. Wen T, Jiang W (2019) Identifying influential nodes based on fuzzy local dimension in complex networks. Chaos, Solitons Fractals 119:332–342. https://doi.org/10.1016/j.chaos.2019.01.011

    Article  MathSciNet  MATH  Google Scholar 

  31. Li C, Wang L, Sun S, Xia C (2018) Identification of influential spreaders based on classified neighbors in real-world complex networks. Appl Math Comput 320:512–523. https://doi.org/10.1016/j.amc.2017.10.001

    Article  MathSciNet  MATH  Google Scholar 

  32. Mo H, Deng Y (2019) Identifying node importance based on evidence theory in complex networks. Physica A: Stat Mech its Appl 529:121538. https://doi.org/10.1016/j.physa.2019.121538

    Article  Google Scholar 

  33. Yang Y, Yu L, Zhou Z, Chen Y, Kou T (2019) Node importance ranking in complex networks based on multicriteria decision making. Math Probl Eng 2019:1–12

    Google Scholar 

  34. Zhao J, Song Y, Liu F, Deng Y (2020) The identification of influential nodes based on structure similarity. Connection ence 19:1–18

    Google Scholar 

  35. Liu F, Wang Z, Deng Y (2020) GMM: a generalized mechanics model for identifying the importance of nodes in complex networks.105464

  36. Wen T, Pelusi D, Deng Y (2019) Vital spreaders identification in complex networks with multi-local dimension

  37. Zhao J, Song Y, Deng Y (2020) A novel model to identify the influential nodes: evidence theory centrality. IEEE Access 8:46773–46780

    Article  Google Scholar 

  38. Zhao J, Wang Y, Deng Y (2020) Identifying influential nodes in complex networks from global perspective. Chaos, Solitons Fractals 133:109637. https://doi.org/10.1016/j.chaos.2020.109637

    Article  MathSciNet  Google Scholar 

  39. Petermann T, De los Rios P (2004) Role of clustering and gridlike ordering in epidemic spreading. Phys Rev E Stat Nonlinear Soft Matter Phys 69(6 Pt 2):066116. https://doi.org/10.1103/PhysRevE.69.066116

    Article  Google Scholar 

  40. Zhou T, Yan G, Wang BH (2005) Maximal planar networks with large clustering coefficient and power-law degree distribution. Phys Rev E Stat Nonlinear Soft Matter Phys 71(4 Pt 2):046141

    Article  Google Scholar 

  41. Zareie A, Sheikhahmadi A, Jalili M, Fasaei M (2020) Finding influential nodes in social networks based on neighborhood correlation coefficient. Knowledge-based systems:105580. https://doi.org/10.1016/j.knosys.2020.105580

  42. Liu Y, Tang M, Zhou T, Do Y (2016) Identify influential spreaders in complex networks, the role of neighborhood. Physica A: Stat Mech its Appl 452:289–298. https://doi.org/10.1016/j.physa.2016.02.028

    Article  Google Scholar 

  43. Ma L-l, Ma C, Zhang H-F, Wang B-H (2016) Identifying influential spreaders in complex networks based on gravity formula. Physica A: Stat Mech its Appl 451:205–212. https://doi.org/10.1016/j.physa.2015.12.162

    Article  MATH  Google Scholar 

  44. Morone F, Makse HA (2015) Influence maximization in complex networks through optimal percolation. Natur 524(7563):65–68. https://doi.org/10.1038/nature14604

    Article  Google Scholar 

  45. Pei S, Muchnik L, Andrade J, José S, Zheng Z, Makse HA (2014) Searching for superspreaders of information in real-world social media. Sci Rep 4

  46. Chen D-B, Gao H, Lü L, Zhou T (2013) Identifying influential nodes in large-scale directed networks: the role of clustering. PLoS One 8(10):e77455. https://doi.org/10.1371/journal.pone.0077455

    Article  Google Scholar 

  47. Li M, Zhang R, Hu R, Yang F, Yao Y, Yuan Y (2018) Identifying and ranking influential spreaders in complex networks by combining a local-degree sum and the clustering coefficient. IJMPB 32(06):1850118. https://doi.org/10.1142/s0217979218501187

    Article  MATH  Google Scholar 

  48. Gao S, Ma J, Chen Z, Wang G, Xing C (2014) Ranking the spreading ability of nodes in complex networks based on local structure. Physica A: Stat Mech its Appl 403:130–147. https://doi.org/10.1016/j.physa.2014.02.032

    Article  MATH  Google Scholar 

  49. Kendall GM (1938) A new measure of rank correlation. Biome 30(1–2):81–93

    MATH  Google Scholar 

  50. Kendall GM (1945) The treatment of ties in ranking problems. Biome 33(3):239–251

    MathSciNet  MATH  Google Scholar 

  51. Knight RW (1966) A computer method for calculating Kendall’s tau with ungrouped data. Publ Am Stat Assoc 61(314):436–439

    Article  Google Scholar 

  52. Zhu T, Wang B, Wu B, Zhu C (2014) Maximizing the spread of influence ranking in social networks. Inf Sci 278:535–544. https://doi.org/10.1016/j.ins.2014.03.070

    Article  MathSciNet  Google Scholar 

  53. Hébert-Dufresne L, Allard A, Young J-G, Dubé LJ (2013) Global efficiency of local immunization on complex networks. Sci Rep 3:2171

    Article  Google Scholar 

Download references

Acknowledgments

We would like to acknowledge springer nature editorial team for editing this manuscript. This work is supported by the Nature Science Foundation of China (No. 71772107).

Funding

This work is supported by the Nature Science Foundation of China (No. 71772107).

Author information

Authors and Affiliations

  1. Shandong Province Key Laboratory of Wisdom Mine Information Technology, College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, 266590, China

    Liqing Qiu, Jianyi Zhang & Xiangbo Tian

Authors
  1. Liqing Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianyi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiangbo Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liqing Qiu.

Ethics declarations

Conflict of interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “Ranking influential nodes in complex networks based on local and global structures”.

Code availability

Not applicable.

Additional information

Publisher’s note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qiu, L., Zhang, J. & Tian, X. Ranking influential nodes in complex networks based on local and global structures. Appl Intell 51, 4394–4407 (2021). https://doi.org/10.1007/s10489-020-02132-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-020-02132-1

Keywords

Search

Navigation