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.
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Goh K I, Cusick M E, Valle D, et al. The human disease network. Proc Natl Acad Sci USA, 2007, 104: 8685–8690
Guille A, Hacid H, Favre C, et al. Information diffusion in online social networks: a survey. ACM SIGMOD Rec, 2013, 42: 17–28
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
Yang L, Li Z, Giua A. Containment of rumor spread in complex social networks. Inf Sci, 2020, 506: 113–130
Lü L, Medo M, Yeung C H, et al. Recommender systems. Phys Reports, 2012, 519: 1–49
Lü L, Chen D, Ren X L, et al. Vital nodes identification in complex networks. Phys Reports, 2016, 650: 1–63
Newman M. Networks. Oxford: Oxford University Press, 2018
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
Freeman L C. A set of measures of centrality based on betweenness. Sociometry, 1977, 40: 35–41
Bonacich P. Factoring and weighting approaches to status scores and clique identification. J Math Sociol, 1972, 2: 113–120
Brin S, Page L. The anatomy of a large-scale hypertextual web search engine. Comput Networks ISDN Syst, 1998, 30: 107–117
Li P X, Ren Y Q, Xi Y M. An importance measure of actors (set) within a network. Syst Eng, 2004, 22: 13–20
Morone F, Makse H A. Influence maximization in complex networks through optimal percolation. Nature, 2015, 524: 65–68
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
Qiu Z, Fan T, Li M, et al. Identifying vital nodes by Achlioptas process. New J Phys, 2021, 23: 033036
Liu J G, Lin J H, Guo Q, et al. Locating influential nodes via dynamics-sensitive centrality. Sci Rep, 2016, 6: 21380
Kitsak M, Gallos L K, Havlin S, et al. Identification of influential spreaders in complex networks. Nat Phys, 2010, 6: 888–893
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
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
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
Sizemore A E, Giusti C, Kahn A, et al. Cliques and cavities in the human connectome. J Comput Neurosci, 2018, 44: 115–145
Lizier J T, Atay F M, Jost J. Information storage, loop motifs, and clustered structure in complex networks. Phys Rev E, 2012, 86: 026110
Petermann T, Rios P D L. Role of clustering and gridlike ordering in epidemic spreading. Phys Rev E, 2004, 69: 066116
Fan T, Lü L, Shi D, et al. Characterizing cycle structure in complex networks. Commun Phys, 2021, 4: 272
Korn A, Schubert A, Telcs A. Lobby index in networks. Phys A-Stat Mech Its Appl, 2009, 388: 2221–2226
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
Freeman L C. Centrality in social networks conceptual clarification. Soc Networks, 1978, 1: 215–239
Anderson R M, May R M. Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press, 1992
Liu J G, Wang Z Y, Guo Q, et al. Identifying multiple influential spreaders via local structural similarity. Europhys Lett, 2017, 119: 18001
Lü L, Zhang Y C, Yeung C H, et al. Leaders in social networks, the delicious case. Plos One, 2011, 6: e21202
Hirsch J E. An index to quantify an individual’s scientific research output. Proc Natl Acad Sci USA, 2005, 102: 16569–16572
Hotelling H. Simplified calculation of principal components. Psychometrika, 1936, 1: 27–35
Watts D J, Strogatz S H. Collective dynamics of ‘small-world’ networks. Nature, 1998, 393: 440–442
Opsahl T, Agneessens F, Skvoretz J. Node centrality in weighted networks: generalizing degree and shortest paths. Soc Networks, 2010, 32: 245–251
Jeong H, Mason S P, Barabási A L, et al. Lethality and centrality in protein networks. Nature, 2001, 411: 41–42
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
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
Spring N, Mahajan R, Wetherall D. Measuring ISP topologies with rocketfuel. ACM SIGCOMM Comput Commun Rev, 2002, 32: 133–145
Pastor-Satorras R, Castellano C, van Mieghem P, et al. Epidemic processes in complex networks. Rev Mod Phys, 2015, 87: 925–979
Newman M E J. Clustering and preferential attachment in growing networks. Phys Rev E, 2001, 64: 025102
Kendall M G. A new measure of rank correlation. Biometrika, 1938, 30: 81–93
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
Rodriguez A, Laio A. Clustering by fast search and find of density peaks. Science, 2014, 344: 1492–1496
Zhao X Y, Huang B, Tang M, et al. Identifying effective multiple spreaders by coloring complex networks. Europhys Lett, 2015, 108: 68005
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
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
Bondy J A, Murty U S R. Graph Theory With Applications. London: Macmillan Press, 1976
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.
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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.
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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
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DOI: https://doi.org/10.1007/s11432-022-3715-4