Predicting the evolution of spreading on complex networks

Due to the wide applications, spreading processes on complex networks have been intensively studied. However, one of the most fundamental problems has not yet been well addressed: predicting the evolution of spreading based on a given snapshot of the propagation on networks. With this problem solved, one can accelerate or slow down the spreading in advance if the predicted propagation result is narrower or wider than expected. In this paper, we propose an iterative algorithm to estimate the infection probability of the spreading process and then apply it to a mean-field approach to predict the spreading coverage. The validation of the method is performed in both artificial and real networks. The results show that our method is accurate in both infection probability estimation and spreading coverage prediction.

[1]  Aravind Srinivasan,et al.  Modelling disease outbreaks in realistic urban social networks , 2004, Nature.

[2]  Boleslaw K. Szymanski,et al.  Accelerating consensus on co-evolving networks: the effect of committed individuals , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Matt J Keeling,et al.  Using conservation of pattern to estimate spatial parameters from a single snapshot , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[4]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[5]  R. May,et al.  How Viruses Spread Among Computers and People , 2001, Science.

[6]  Hui Gao,et al.  Identifying Influential Nodes in Large-Scale Directed Networks: The Role of Clustering , 2013, PloS one.

[7]  D. Helbing,et al.  The Hidden Geometry of Complex, Network-Driven Contagion Phenomena , 2013, Science.

[8]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[9]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[10]  J. Gleeson,et al.  Seed size strongly affects cascades on random networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Amos Maritan,et al.  Size and form in efficient transportation networks , 1999, Nature.

[12]  Boleslaw K. Szymanski,et al.  Threshold-limited spreading in social networks with multiple initiators , 2013, Scientific Reports.

[13]  Su Deng,et al.  Hop limited epidemic-like information spreading in mobile social networks with selfish nodes , 2013 .

[14]  Jon M. Kleinberg,et al.  The link-prediction problem for social networks , 2007, J. Assoc. Inf. Sci. Technol..

[15]  Sergey N. Dorogovtsev,et al.  Critical phenomena in complex networks , 2007, ArXiv.

[16]  Antoine Allard,et al.  Percolation on random networks with arbitrary k-core structure. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Jure Leskovec,et al.  Defining and evaluating network communities based on ground-truth , 2012, Knowledge and Information Systems.

[18]  Kim Sneppen,et al.  A Minimal Model for Multiple Epidemics and Immunity Spreading , 2010, PloS one.

[19]  Matt J Keeling,et al.  Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[20]  A-L Barabási,et al.  Structure and tie strengths in mobile communication networks , 2006, Proceedings of the National Academy of Sciences.

[21]  Alberto Rosso,et al.  Spatial extent of an outbreak in animal epidemics , 2013, Proceedings of the National Academy of Sciences.

[22]  Yi-Cheng Zhang,et al.  Adaptive model for recommendation of news , 2009, ArXiv.

[23]  M. Ángeles Serrano,et al.  Structural Efficiency of Percolated Landscapes in Flow Networks , 2007, PloS one.

[24]  Adilson E Motter.  Cascade control and defense in complex networks. , 2004, Physical review letters.

[25]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[26]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[27]  Linyuan Lu,et al.  Link Prediction in Complex Networks: A Survey , 2010, ArXiv.

[28]  J. Benoit,et al.  Pair approximation models for disease spread , 2005, q-bio/0510005.

[29]  Lubos Buzna,et al.  Decelerated spreading in degree-correlated networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[31]  A. Bishop,et al.  Link operations for slowing the spread of disease in complex networks , 2011 .

[32]  Giulio Cimini,et al.  Enhancing topology adaptation in information-sharing social networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Albert-László Barabási,et al.  Quantifying Long-Term Scientific Impact , 2013, Science.

[34]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[35]  Lev Muchnik,et al.  Identifying influential spreaders in complex networks , 2010, 1001.5285.

[36]  Yi-Cheng Zhang,et al.  Trend prediction in temporal bipartite networks: the case of Movielens, Netflix, and Digg , 2013, Adv. Complex Syst..

[37]  Martin Vetterli,et al.  Locating the Source of Diffusion in Large-Scale Networks , 2012, Physical review letters.

[38]  A. D. Jackson,et al.  Citation networks in high energy physics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Damon Centola,et al.  The Spread of Behavior in an Online Social Network Experiment , 2010, Science.

[40]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[41]  Yi-Cheng Zhang,et al.  Leaders in Social Networks, the Delicious Case , 2011, PloS one.

[42]  Duanbing Chen,et al.  The small world yields the most effective information spreading , 2011, ArXiv.

[43]  Antoine Allard,et al.  Global efficiency of local immunization on complex networks , 2012, Scientific Reports.

[44]  Jaewook Joo,et al.  Pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[46]  Christos Faloutsos,et al.  Graph evolution: Densification and shrinking diameters , 2006, TKDD.

[47]  Marco Tomassini,et al.  Worldwide spreading of economic crisis , 2010, 1008.3893.

[48]  T. Valente,et al.  Accelerating the Diffusion of Innovations Using Opinion Leaders , 1999 .

[49]  Alexandre Proutière,et al.  Hop limited flooding over dynamic networks , 2011, 2011 Proceedings IEEE INFOCOM.

[50]  Angélica S. Mata,et al.  Heterogeneous pair-approximation for the contact process on complex networks , 2014, 1402.2832.