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Diffusion dynamics and information spreading in multilayer networks: An overview

Abstract

Recent years have seen multilayer networks taking the helm at network science research. Diffusion dynamics and information spreading in multilayer networks are thereby two of the most explored topics, with numerous applications in social, technological, and biological systems. Almost a decade ago, groundbreaking research has shown that even small and seemingly unimportant changes in one network layer can have catastrophic consequences in many other network layers. Such failure cascades across different network layers can, for example, shut down power grids, arrest traffic, idle virality, or impair cooperation. Different spreading processes are often the common denominator of such phenomena, and in the light of their importance, we here present a brief overview of this subject.

References

  1. A. Barrat, M. Barthélemy, A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008).

  2. M.E.J. Newman, Networks: An Introduction (Oxford University Press, Oxford, 2010).

  3. E. Estrada, The Structure of Complex Networks: Theory and Applications (Oxford University Press, Oxford, 2012).

  4. A.-L. Barabási, Network Science (Cambridge University Press, Cambridge, 2015).

  5. D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998).

    ADS  Google Scholar 

  6. A.-L. Barabási, R. Albert, Science 286, 509 (1999).

    ADS  MathSciNet  Google Scholar 

  7. M. Girvan, M.E. Newman, Proc. Natl. Acad. Sci. USA 99, 7821 (2002).

    ADS  MathSciNet  Article  Google Scholar 

  8. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002).

    ADS  MathSciNet  Article  Google Scholar 

  9. M.E.J. Newman, SIAM Rev. 45, 167 (2003).

    ADS  MathSciNet  Article  Google Scholar 

  10. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D. Hwang, Phys. Rep. 424, 175 (2006).

    ADS  MathSciNet  Google Scholar 

  11. S. Fortunato, Phys. Rep. 486, 75 (2010).

    ADS  MathSciNet  Article  Google Scholar 

  12. M. Barthelemy, Phys. Rep. 499, 1 (2011).

    ADS  MathSciNet  Article  Google Scholar 

  13. P. Holme, J. Saramäki, Phys. Rep. 519, 97 (2012).

    ADS  Article  Google Scholar 

  14. S. Boccaletti, G. Bianconi, R. Criado, C. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang, M. Zanin, Phys. Rep. 544, 1 (2014).

    ADS  MathSciNet  Article  Google Scholar 

  15. M. Kivelä, A. Arenas, M. Barthelemy, J.P. Gleeson, Y. Moreno, M.A. Porter, J. Complex Networks 2, 203 (2014).

    Article  Google Scholar 

  16. L. Lü, D. Chen, X.-L. Ren, Q.-M. Zhang, Y.-C. Zhang, T. Zhou, Phys. Rep. 650, 1 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  17. T. Gross, B. Blasius, J.R. Soc, Interface 5, 259 (2008).

    Google Scholar 

  18. M. Perc, A. Szolnoki, BioSystems 99, 109 (2010).

    Article  Google Scholar 

  19. S.V. Buldyrev, R. Parshani, G. Paul, H.E. Stanley, S. Havlin, Nature 464, 1025 (2010).

    ADS  Article  Google Scholar 

  20. R. Parshani, S.V. Buldyrev, S. Havlin, Phys. Rev. Lett. 105, 048701 (2010).

    ADS  Article  Google Scholar 

  21. P.J. Mucha, T. Richardson, K. Macon, M.A. Porter, J.-P. Onnela, Science 328, 876 (2010).

    ADS  MathSciNet  Article  Google Scholar 

  22. R. Parshani, S.V. Buldyrev, S. Havlin, Proc. Natl. Acad. Sci. USA 108, 1007 (2011).

    ADS  Article  Google Scholar 

  23. J. Gao, S.V. Buldyrev, H.E. Stanley, S. Havlin, Nat. Phys. 8, 40 (2012).

    Article  Google Scholar 

  24. S. Havlin, D.Y. Kenett, E. Ben-Jacob, A. Bunde, H. Hermann, J. Kurths, S. Kirkpatrick, S. Solomon, J. Portugali, Eur. Phys. J. Special Topics 214, 273 (2012).

    ADS  Article  Google Scholar 

  25. S. Gómez, A. Díaz-Guilera, J. Gómez-Gardeñes, C. Pérez-Vicente, Y. Moreno, A. Arenas, Phys. Rev. Lett. 110, 028701 (2013).

    ADS  Article  Google Scholar 

  26. M. De Domenico, A. Solé-Ribalta, E. Cozzo, M. Kivelä, Y. Moreno, M.A. Porter, S. Gómez, A. Arenas, Phys. Rev. X 3, 041022 (2013).

    Google Scholar 

  27. Z. Wang, L. Wang, A. Szolnoki, M. Perc, Eur. Phys. J. B 88, 124 (2015).

    ADS  Article  Google Scholar 

  28. D.Y. Kenett, M. Perc, S. Boccaletti, Chaos Soliton Fract. 80, 1 (2015).

    ADS  Article  Google Scholar 

  29. Z. Wang, A. Szolnoki, M. Perc, EPL 97, 48001 (2012).

    ADS  Article  Google Scholar 

  30. J. Gómez-Gardeñes, I. Reinares, A. Arenas, L.M. Flora, Sci. Rep. 2, 620 (2012).

    ADS  Article  Google Scholar 

  31. J. Gómez-Gardeñes, C. Gracia-Lázaro, L.M. Flora, Y. Moreno, Phys. Rev. E 86, 056113 (2012).

    ADS  Article  Google Scholar 

  32. B. Wang, X. Chen, L. Wang, J. Stat. Mech. 2012, P11017 (2012).

    Article  Google Scholar 

  33. Z. Wang, A. Szolnoki, M. Perc, Sci. Rep. 3, 1183 (2013).

    ADS  Article  Google Scholar 

  34. Z. Wang, A. Szolnoki, M. Perc, Sci. Rep. 3, 2470 (2013).

    ADS  Article  Google Scholar 

  35. L.-L. Jiang, M. Perc, Sci. Rep. 3, 2483 (2013).

    Article  Google Scholar 

  36. A. Szolnoki, M. Perc, New J. Phys. 15, 053010 (2013).

    ADS  MathSciNet  Article  Google Scholar 

  37. Z. Wang, L. Wang, M. Perc, Phys. Rev. E 89, 052813 (2014).

    ADS  Article  Google Scholar 

  38. F. Battiston, M. Perc, V. Latora, New J. Phys. 19, 073017 (2017).

    ADS  Article  Google Scholar 

  39. C. Shen, C. Chu, L. Shi, M. Jusup, M. Perc, Z. Wang, EPL 124, 48003 (2018).

    Article  Google Scholar 

  40. C. Xia, X. Li, Z. Wang, M. Perc, New J. Phys. 20, 075005 (2018).

    ADS  Article  Google Scholar 

  41. L. Shi, C. Shen, Y. Geng, C. Chu, H. Meng, M. Perc, S. Boccaletti, Z. Wang, Nonlinear Dyn. 96, 49 (2019).

    Article  Google Scholar 

  42. W. Li, A. Bashan, S.V. Buldyrev, Phys. Rev. Lett. 108, 228702 (2012).

    ADS  Article  Google Scholar 

  43. C.D. Brummitt, R.M. D’Souza, E.A. Leicht, Proc. Natl. Acad. Sci. USA 109, E680 (2012).

    ADS  Article  Google Scholar 

  44. J. Nagler, A. Levina, M. Timme, Nat. Phys. 7, 265 (2011).

    Article  Google Scholar 

  45. D. Cellai, E. López, J. Zhou, J.P. Gleeson, G. Bianconi, Phys. Rev. E 88, 052811 (2013).

    ADS  Article  Google Scholar 

  46. R.G. Morris, M. Barthelemy, Phys. Rev. Lett. 109, 128703 (2012).

    ADS  Article  Google Scholar 

  47. X. Sun, J. Lei, M. Perc, J. Kurths, G. Chen, Chaos 21, 016110 (2011).

    ADS  Article  Google Scholar 

  48. C. Granell, S. Gómez, A. Arenas, Phys. Rev. Lett. 111, 128701 (2013).

    ADS  Article  Google Scholar 

  49. X. Huang, J. Gao, S.V. Buldyrev, S. Havlin, H.E. Stanley, Phys. Rev. E 83, 065101(R) (2011).

    ADS  Article  Google Scholar 

  50. D. Zhou, H.E. Stanley, G. D’Agostino, A. Scala, Phys. Rev. E 86, 066103 (2012).

    ADS  Article  Google Scholar 

  51. E. Cozzo, A. Arenas, Y. Moreno, Phys. Rev. E 86, 036115 (2012).

    ADS  Article  Google Scholar 

  52. V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, Phys. Rev. Lett. 111, 058701 (2013).

    ADS  Article  Google Scholar 

  53. G. Bianconi, Phys. Rev. E 87, 062806 (2013).

    ADS  Article  Google Scholar 

  54. F. Radicchi, A. Arenas, Nat. Phys. 9, 717 (2013).

    Article  Google Scholar 

  55. A. Arenas, A. Daz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  56. J.A. Almendral, A. Daz-Guilera, New J. Phys. 9, 187 (2007).

    ADS  Article  Google Scholar 

  57. M. Barahona, L.M. Pecora, Phys. Rev. Lett. 89, 054101 (2002).

    ADS  Article  Google Scholar 

  58. S. Jalan, G. Zhu, B. Li, Phys. Rev. E 84, 046107 (2011).

    ADS  Article  Google Scholar 

  59. E. Estrada, N. Hatano, M. Benzi, Phys. Rep. 514, 89 (2012).

    ADS  MathSciNet  Article  Google Scholar 

  60. P. Van Mieghem, Graph spectra for complex networks (Cambridge University Press, Cambridge, 2010).

  61. F. Geier, W. Barfuss, M. Wiedermann, J. Kurths, J.F. Donges, Eur. Phys. J. Special Topics 228, 2357 (2019).

    Google Scholar 

  62. Y. Feng, A.J.M. Khalaf, F.E. Alsaadi, T. Hayat, V.-T. Pham, Eur. Phys. J. Special Topics 228, 2371 (2019).

    Google Scholar 

  63. N.S. Frolov, V.A. Maksimenko, M.V. Khramova, A.N. Pisarchik, A.E. Hramov, Eur. Phys. J. Special Topics 228, 2381 (2019).

    Google Scholar 

  64. Z. Wang, F.E. Alsaadi, V.-T. Pham, Eur. Phys. J. Special Topics 228, 2391 (2019).

    Article  Google Scholar 

  65. Y. Shaverdi, S. Panahi, T. Kapitaniak, S. Jafari, Eur. Phys. J. Special Topics 228, 2405 (2019).

    Google Scholar 

  66. X. Li, T. Xu, J. Li, Eur. Phys. J. Special Topics 228, 2419 (2019).

    Google Scholar 

  67. S. Kundu, S. Majhi, D. Ghosh, Eur. Phys. J. Special Topics 228, 2429 (2019).

    Google Scholar 

  68. B.K. Bera, S. Rakshit, D. Ghosh, Eur. Phys. J. Special Topics 228, 2441 (2019).

    Google Scholar 

  69. M. Ge, L. Lu, Y. Xu, X. Zhan, L. Yang, Y. Jia, Eur. Phys. J. Special Topics 228, 2455 (2019).

    Google Scholar 

  70. F. Parastesh, C.-Y. Chen, H. Azarnoush, S. Jafari, B. Hatef, Eur. Phys. J. Special Topics 228, 2465 (2019).

    Google Scholar 

  71. F. An, X. Gao, J. Guan, M. Jiang, Q. Liu, Eur. Phys. J. Special Topics 228, 2475 (2019).

    Google Scholar 

  72. M. Pósfai, N. Braun, B.A. Beisner, B. McCowan, R.M. D’Souza, New J. Phys. 21, 055001 (2019).

    ADS  Article  Google Scholar 

  73. B. Min, M. San Miguel, New J. Phys. 21, 035004 (2019).

    ADS  Article  Google Scholar 

  74. J. Choi, K.-I. Goh, New J. Phys. 21, 035005 (2019).

    ADS  Article  Google Scholar 

  75. J. Van Lidth, T. de Jeude, G.Caldarelli Aste, New J. Phys. 21, 025002 (2019).

    ADS  Article  Google Scholar 

  76. J.D. O’Brien, I.K. Dassios, J.P. Gleeson, New J. Phys. 21, 025001 (2019).

    ADS  Article  Google Scholar 

  77. R.-R. Liu, C.-X. Jia, Y.-C. Lai, New J. Phys. 21, 045002 (2019).

    ADS  Article  Google Scholar 

  78. G. Cencetti, F. Battiston, New J. Phys. 21, 035006 (2019).

    ADS  Article  Google Scholar 

  79. H. Wang, C. Qu, C. Jiao, W. Rusze, New J. Phys. 21, 035001 (2019).

    ADS  Article  Google Scholar 

  80. Y. Zhou, J. Zhou, G. Chen, H.E. Stanley, New J. Phys. 21, 035002 (2019).

    ADS  Article  Google Scholar 

  81. A. Solé-Ribalta, A. Arenas, S. Gómez, New J. Phys. 21, 035003 (2019).

    ADS  Article  Google Scholar 

  82. J. Liu, Y. Fan, J. Zhang, Z. Di, New J. Phys. 21, 015007 (2019).

    ADS  Article  Google Scholar 

  83. A.D. Kachhvah, S. Jalan, New J. Phys. 21, 015006 (2019).

    Article  Google Scholar 

  84. H.-J. Li, L. Wang, New J. Phys. 21, 015005 (2019).

    ADS  Article  Google Scholar 

  85. E. Estrada, New J. Phys. 21, 015004 (2019).

    ADS  Article  Google Scholar 

  86. D. Han, X. Li, New J. Phys. 21, 015002 (2019).

    ADS  Article  Google Scholar 

  87. N. An, H. Chen, C. Ma, H. Zhang, New J. Phys. 20, 125006 (2018).

    Article  Google Scholar 

  88. W. Dang, Z. Gao, D. Lv, M. Liu, Q. Cai, X. Hong, New J. Phys. 20, 125005 (2018).

    Article  Google Scholar 

  89. L. Valdez, H.A. Rêgo, H. Stanley, S. Havlin, L. Braunstein, New J. Phys. 20, 125003 (2018).

    Article  Google Scholar 

  90. X. Zhu, H. Tian, X. Chen, W. Wang, S. Cai, New J. Phys. 20, 125002 (2018).

    ADS  Article  Google Scholar 

  91. G.F. de Arruda, E. Cozzo, F.A. Rodrigues, Y. Moreno, New J. Phys. 20, 095004 (2018).

    Article  Google Scholar 

  92. H.-C.H. Chang, F. Fu, New J. Phys. 20, 095001 (2018).

    ADS  Article  Google Scholar 

  93. E. Pitsik, V. Makarov, D. Kirsanov, N. Frolov, M. Goremyko, X. Li, Z. Wang, A. Hramov, S. Boccaletti, New J. Phys. 20, 075004 (2018).

    ADS  Article  Google Scholar 

  94. C. Xia, X. Li, Z. Wang, M. Perc, New J. Phys. 20, 075005 (2018).

    ADS  Article  Google Scholar 

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Perc, M. Diffusion dynamics and information spreading in multilayer networks: An overview. Eur. Phys. J. Spec. Top. 228, 2351–2355 (2019). https://doi.org/10.1140/epjst/e2019-900201-4

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