Abstract
A long-term common belief in complex networks is that, the most connected nodes are the most efficient spreaders. However, recent investigations on real-world complex networks show that the most influential spreaders are those with the highest k-shell values. It is well-known that, many real-world complex networks have scale free (SF), small world (SW) properties, therefore, identification of influential spreaders in general artificial SF, SW as well as random networks will be more appealing. This research finds that, for artificial ER and SW networks, degree is more reliable than k-shell in predicting the outcome of spreading. However, for artificial SF networks, k-shell is remarkably reliable than degree and betweeness, which indicate that the four recently investigated real-world networks [Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A, Identification of influential spreaders in complex networks, Nat. Phys., 2010, 6: 888–893.] are more similar to scale free ones. Moreover, the investigations also indicate us an optimal dissemination strategy in networks with scale free property. That is, starting from moderate-degree-nodes will be ok and even more economical, since one can derive roughly similar outcome with starting from hubs.
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References
Bullmore E and Sporns O, Complex brain networks: Graph theoretical analysis of structural and functional systems, Nat. Rev., 2009, 10: 186–198.
May R M and Lloyd A L, Infection dynamics on scale-free networks, Phys. Rev. E, 2001, 64: art.no. 066112.
Lloyd A L and May R M, How virus spread among computers and people, Science, 2001, 292: 1316–1317.
Xu X, Peng H, Wang X, and Wang Y, Epidemic spreading with time delay in complex networks, Physica A, 2006, 367: 525–530.
Nekovee M, Moreno Y, Bianconi G, and Marsili M, Theory of rumour spreading in complex social networks, Physica A, 2007, 374: 457–470.
Chen J, Zhang H, Guan Z, and Li T, Epidemic spreading on networks with overlapping community structure, Physica A, 2012, 391: 1848–1854.
Ni S, Weng W, and Zhang H, Modeling the effects of social impact on epidemic spreading in complex networks, Physica A, 2011, 390: 4528–4534.
Anderson R M, May R M, and Anderson B, Infectious Diseases of Humans: Dynamics and Control, Oxford Science Publications, 1992.
Hethcote H W, The mathematics of infectious diseases, SIAM Rev., 2000, 42: 599–653.
Fan W and Yeung K H, Online social networks-Paradise of computer viruses, Physica A, 2011, 390: 189–197.
Christley R M, Pinchbeck G L, Bowers R G, Clancy D, French N P, Bennett R, and Turner J, Infection in social networks: Using network analysis to identify high-risk individuals, Am. J. Epidemiol., 2005, 162: 1024–1031.
Liu J, Wu J, and Yang Z R, The spread of infectious disease on complex networks with householdstructure, Physica A, 2004, 341: 273–280.
Pastor-Satorras R and Vespignani A, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 2001, 86: 3200–3203.
Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, and Makse H A, Identification of influential spreaders in complex networks, Nat. Phys., 2010, 6: 888–893.
Chen D, Lü L, Shang M, Zhang Y, and Zhou T, Identifying influential nodes in complex networks, Physica A, 2012, 391: 1777–1787.
Kuhnert M, Geier C, Elger C E, and Lehnertz K, Identifying important nodes in weighted functional brain networks: A comparison of different centrality approaches, Chaos, 2012, 22: art. no. 023142.
Freeman L C, Centrality in social networks: Conceptual clarification, Social Networks, 1979, 1: 215–239.
Carmi S, Havlin S, Kirkpatrick S, Shavitt Y, and Shir E, A model of Internet topology using k-shell decomposition, Proc. Natl. Acad. Sci. USA, 2007, 104: 11150–11154.
Centola D, The spread of behavior in an online social network experiment, Science, 2010, 329: 1194–1197.
Barabási A and Albert R, Emergence of scaling in random networks, Science, 1999, 286: 509–512.
Watts D J and Strogatz S H, Collective dynamics of ‘small world’ networks, Nature, 1998, 393: 440–442.
Fan Z, Chen G, and Zhang Y, A comprehensive multi-local-world model for complex networks, Phys. Lett. A, 2009, 373: 1601–1605.
Bollobás B, Random Graphs, 2nd Edition, Cambridge University Press, 2001.
Pennock D M, Flake G W, Lawrence S, Glover E J, and Giles C L, Winners don’t take all: Characterizing the competition for links on the web, Proc. Natl. Acad. Sci. USA, 2002, 99: 5207–5211.
Wang X, Li X, and Chen G, Complex Networks Theory and Its Applications, Tsinghua University Press, 2006 (in chinese).
Wilensky U, NetLogo, http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL, 1999.
Hu H and Wang X, Unified index to quantifying heterogeneity of complex networks, Physica A, 2008, 387: 3769–3780.
Wasserman S and Faust K, Social Network Analysis: Methods and Applications, Cambridge University Press, 1994.
Shannon C E, Prediction and entropy of printed English, Bell Syst. Tech. J., 1951, 30: 50–64.
Pastor-Satorras R and Vespignani A, Epidemics and immunization in scale-free networks, Handbook of Graphs and Networks (eds. by Bornholdt S and Schuster H G), Wileyvch Publisher, Berlin, 2003.
Wang X and Chen G, Complex networks: Small-world, scale-free and beyond, IEEE Circuits and Systems Magazine, 2003, 3: 6–20.
Pastor-Satorras R and Vespignani A, Epidemic spreading in scalefree networks, Phys. Rev. Lett., 2001, 86: 3200–3203.
Pastor-Satorras R and Vespignani A, Epidemic dynamics and endemic states in complex networks, Phys. Rev. E, 2001, 63: art.no. 066117.
Lü J and Chen G, A time-varying complex dynamical network model and its controlled synchronization criteria, IEEE Trans. Automat. Control, 2005, 50: 841–846.
Liu H, Lu J, Lü J, and Hill D J, Structure identification of uncertain general complex dynamical networks with time delay, Automatica, 2009, 45: 1799–1807.
Wang P, Lü J, and Ogorzalek M J, Global relative parameter sensitivities of the feed-forward loops in genetic networks, Neurocomput., 2012, 78: 155–165.
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This research is supported by the National Natural Science Foundation of China under Grant Nos. 11172215, 61304151, 61174028, China-Australia Health and HIV/AIDS Facility (FA36 EID101), and the Science Foundation of Henan University under Grant No. 2012YBZR007.
This paper was recommended for publication by Editor LÜ Jinhu.
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Wang, P., Tian, C. & Lu, Ja. Identifying influential spreaders in artificial complex networks. J Syst Sci Complex 27, 650–665 (2014). https://doi.org/10.1007/s11424-014-2236-4
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DOI: https://doi.org/10.1007/s11424-014-2236-4