Skip to main content
SpringerLink
Log in

Cost effective approach to identify multiple influential spreaders based on the cycle structure in networks

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

Identifying influential spreaders has theoretical and practical significance in complex networks. Traditional centrality methods can efficiently find a single spreader, but it could lead to influence redundancy and high initializing costs when used to identify a set of multiple spreaders. A cycle structure is one of the most crucial reasons for the complexity of a network and the cornerstone of the feedback effect. From this novel perspective, we propose a new method based on basic cycles in networks to identify multiple influential spreaders with superior spreading performance and low initializing costs. Experiments on six empirical networks show that the spreaders selected by the proposed method are more scattered in the network and yield the best spreading performance compared with those on seven well-known methods. Importantly, the proposed method is the most cost effective under the same spreading performance. The cycle-based method has the advantage of generating multiple solutions. Our work provides new insights into identifying multiple spreaders and hence can benefit wide applications in practical scenarios.

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

Similar content being viewed by others

References

  1. Goh K I, Cusick M E, Valle D, et al. The human disease network. Proc Natl Acad Sci USA, 2007, 104: 8685–8690

    Article  Google Scholar 

  2. Guille A, Hacid H, Favre C, et al. Information diffusion in online social networks: a survey. ACM SIGMOD Rec, 2013, 42: 17–28

    Article  Google Scholar 

  3. Kempe D, Kleinberg J, Tardos E. Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, 2003. 137–146

  4. Yang L, Li Z, Giua A. Containment of rumor spread in complex social networks. Inf Sci, 2020, 506: 113–130

    Article  MathSciNet  Google Scholar 

  5. Lü L, Medo M, Yeung C H, et al. Recommender systems. Phys Reports, 2012, 519: 1–49

    Article  Google Scholar 

  6. Lü L, Chen D, Ren X L, et al. Vital nodes identification in complex networks. Phys Reports, 2016, 650: 1–63

    Article  MathSciNet  Google Scholar 

  7. Newman M. Networks. Oxford: Oxford University Press, 2018

    Book  MATH  Google Scholar 

  8. Fan T, Li H, Ren X L, et al. The rise and fall of countries on world trade web: a network perspective. Int J Mod Phys C, 2021, 32: 2150121

    Article  MathSciNet  Google Scholar 

  9. Freeman L C. A set of measures of centrality based on betweenness. Sociometry, 1977, 40: 35–41

    Article  Google Scholar 

  10. Bonacich P. Factoring and weighting approaches to status scores and clique identification. J Math Sociol, 1972, 2: 113–120

    Article  Google Scholar 

  11. Brin S, Page L. The anatomy of a large-scale hypertextual web search engine. Comput Networks ISDN Syst, 1998, 30: 107–117

    Article  Google Scholar 

  12. Li P X, Ren Y Q, Xi Y M. An importance measure of actors (set) within a network. Syst Eng, 2004, 22: 13–20

    Google Scholar 

  13. Morone F, Makse H A. Influence maximization in complex networks through optimal percolation. Nature, 2015, 524: 65–68

    Article  Google Scholar 

  14. Morone F, Min B, Bo L, et al. Collective influence algorithm to find influencers via optimal percolation in massively large social media. Sci Rep, 2016, 6: 1–11

    Article  Google Scholar 

  15. Qiu Z, Fan T, Li M, et al. Identifying vital nodes by Achlioptas process. New J Phys, 2021, 23: 033036

    Article  MathSciNet  Google Scholar 

  16. Liu J G, Lin J H, Guo Q, et al. Locating influential nodes via dynamics-sensitive centrality. Sci Rep, 2016, 6: 21380

    Article  Google Scholar 

  17. Kitsak M, Gallos L K, Havlin S, et al. Identification of influential spreaders in complex networks. Nat Phys, 2010, 6: 888–893

    Article  Google Scholar 

  18. Wang X, Zhang X, Zhao C, et al. Effectively identifying multiple influential spreaders in term of the backward-forward propagation. Phys A-Stat Mech Its Appl, 2018, 512: 404–413

    Article  Google Scholar 

  19. Ji S, Lü L, Yeung C H, et al. Effective spreading from multiple leaders identified by percolation in the susceptible-infected-recovered (SIR) model. New J Phys, 2017, 19: 073020

    Article  Google Scholar 

  20. Shi D, Chen G, Thong W W K, et al. Searching for optimal network topology with best possible synchronizability. IEEE Circuits Syst Mag, 2013, 13: 66–75

    Article  Google Scholar 

  21. Sizemore A E, Giusti C, Kahn A, et al. Cliques and cavities in the human connectome. J Comput Neurosci, 2018, 44: 115–145

    Article  MathSciNet  MATH  Google Scholar 

  22. Lizier J T, Atay F M, Jost J. Information storage, loop motifs, and clustered structure in complex networks. Phys Rev E, 2012, 86: 026110

    Article  Google Scholar 

  23. Petermann T, Rios P D L. Role of clustering and gridlike ordering in epidemic spreading. Phys Rev E, 2004, 69: 066116

    Article  Google Scholar 

  24. Fan T, Lü L, Shi D, et al. Characterizing cycle structure in complex networks. Commun Phys, 2021, 4: 272

    Article  Google Scholar 

  25. Korn A, Schubert A, Telcs A. Lobby index in networks. Phys A-Stat Mech Its Appl, 2009, 388: 2221–2226

    Article  Google Scholar 

  26. Lü L, Zhou T, Zhang Q M, et al. The H-index of a network node and its relation to degree and coreness. Nat Commun, 2016, 7: 10168

    Article  Google Scholar 

  27. Freeman L C. Centrality in social networks conceptual clarification. Soc Networks, 1978, 1: 215–239

    Article  Google Scholar 

  28. Anderson R M, May R M. Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press, 1992

    Google Scholar 

  29. Liu J G, Wang Z Y, Guo Q, et al. Identifying multiple influential spreaders via local structural similarity. Europhys Lett, 2017, 119: 18001

    Article  Google Scholar 

  30. Lü L, Zhang Y C, Yeung C H, et al. Leaders in social networks, the delicious case. Plos One, 2011, 6: e21202

    Article  Google Scholar 

  31. Hirsch J E. An index to quantify an individual’s scientific research output. Proc Natl Acad Sci USA, 2005, 102: 16569–16572

    Article  MATH  Google Scholar 

  32. Hotelling H. Simplified calculation of principal components. Psychometrika, 1936, 1: 27–35

    Article  MATH  Google Scholar 

  33. Watts D J, Strogatz S H. Collective dynamics of ‘small-world’ networks. Nature, 1998, 393: 440–442

    Article  MATH  Google Scholar 

  34. Opsahl T, Agneessens F, Skvoretz J. Node centrality in weighted networks: generalizing degree and shortest paths. Soc Networks, 2010, 32: 245–251

    Article  Google Scholar 

  35. Jeong H, Mason S P, Barabási A L, et al. Lethality and centrality in protein networks. Nature, 2001, 411: 41–42

    Article  Google Scholar 

  36. Rossi R, Ahmed N. The network data repository with interactive graph analytics and visualization. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence, Austin, 2015. 29: 4292–4293

  37. Rozemberczki B, Sarkar R. Characteristic functions on graphs: birds of a feather, from statistical descriptors to parametric models. In: Proceedings of the 29th ACM International Conference on Information & Knowledge Management, 2020. 1325–1334

  38. Spring N, Mahajan R, Wetherall D. Measuring ISP topologies with rocketfuel. ACM SIGCOMM Comput Commun Rev, 2002, 32: 133–145

    Article  Google Scholar 

  39. Pastor-Satorras R, Castellano C, van Mieghem P, et al. Epidemic processes in complex networks. Rev Mod Phys, 2015, 87: 925–979

    Article  MathSciNet  Google Scholar 

  40. Newman M E J. Clustering and preferential attachment in growing networks. Phys Rev E, 2001, 64: 025102

    Article  Google Scholar 

  41. Kendall M G. A new measure of rank correlation. Biometrika, 1938, 30: 81–93

    Article  MATH  Google Scholar 

  42. Ma L, Ma C, Zhang H F, et al. Identifying influential spreaders in complex networks based on gravity formula. Phys A-Stat Mech Appl, 2016, 451: 205–212

    Article  MATH  Google Scholar 

  43. Rodriguez A, Laio A. Clustering by fast search and find of density peaks. Science, 2014, 344: 1492–1496

    Article  Google Scholar 

  44. Zhao X Y, Huang B, Tang M, et al. Identifying effective multiple spreaders by coloring complex networks. Europhys Lett, 2015, 108: 68005

    Article  Google Scholar 

  45. Guo L, Lin J H, Guo Q, et al. Identifying multiple influential spreaders in term of the distance-based coloring. Phys Lett A, 2016, 380: 837–842

    Article  Google Scholar 

  46. Hu Z L, Liu J G, Yang G Y, et al. Effects of the distance among multiple spreaders on the spreading. Europhys Lett, 2014, 106: 18002

    Article  Google Scholar 

  47. Bondy J A, Murty U S R. Graph Theory With Applications. London: Macmillan Press, 1976

    Book  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. T2293771), STI 2030-Major Projects (Grant No. 2022ZD0211400), and the New Cornerstone Science Foundation through the XPLORER PRIZE.

Author information

Authors and Affiliations

  1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Wenfeng Shi, Shuqi Xu & Linyuan Lü

  2. Institute of Dataspace, Hefei Comprehensive National Science Center, Hefei, 230088, China

    Shuqi Xu

  3. Department of Physics, University of Fribourg, Fribourg, 1700, Switzerland

    Tianlong Fan

  4. Alibaba Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou, 311121, China

    Tianlong Fan

Authors
  1. Wenfeng Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuqi Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tianlong Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Linyuan Lü
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Shuqi Xu or Linyuan Lü.

Additional information

Supporting information

Appendixes A–D. The supporting information is available online at info.scichina.com and link.springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.

Supplementary File

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, W., Xu, S., Fan, T. et al. Cost effective approach to identify multiple influential spreaders based on the cycle structure in networks. Sci. China Inf. Sci. 66, 192203 (2023). https://doi.org/10.1007/s11432-022-3715-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-022-3715-4

Keywords

Search

Navigation