1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Condensed Matter Physics
  4. Volume 10, 2019
  5. Article

Annual Review of Condensed Matter Physics

Volume 10, 2019

Multilayer Networks in a Nutshell

Abstract

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system constituents. During the past two decades, network science has provided many insights in natural, social, biological, and technological systems. However, real systems are often interconnected, with many interdependencies that are not properly captured by single-layer networks. To account for this source of complexity, a more general framework, in which different networks evolve or interact with each other, is needed. These are known as multilayer networks. Here, we provide an overview of the basic methodology used to describe multilayer systems as well as of some representative dynamical processes that take place on top of them. We round off the review with a summary of several applications in diverse fields of science.

Keyword(s): complex systems, diffusion dynamics, spreading processes
Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-031218-013259
2019-03-10
2025-04-19
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/10/1/annurev-conmatphys-031218-013259.html?itemId=/content/journals/10.1146/annurev-conmatphys-031218-013259&mimeType=html&fmt=ahah

Literature Cited

  1. 1.  Anderson PW 1972. Science 177:393–96
     [Google Scholar]
  2. 2.  Falkenburg B, Morrison M 2015. Why More Is Different? Heidelberg: Springer
     [Google Scholar]
  3. 3.  Mack G 2001. Commun. Math. Phys. 219:141
     [Google Scholar]
  4. 4.  Newman M 2010. Networks: An Introduction Oxford, UK: Oxford Univ. Press
     [Google Scholar]
  5. 5.  Kivelä M, Arenas A, Barthelemy M, Gleeson JP, Moreno Y, Porter MA 2014. J. Complex Netw. 2:203–71
     [Google Scholar]
  6. 6.  Barabsi AL 2016. Network Science Cambridge, UK: Cambridge Univ. Press
     [Google Scholar]
  7. 7.  De Domenico M, Solé-Ribalta A, Cozzo E, Kivelä M, Moreno Y et al. 2013. Phys. Rev. X 3:041022
     [Google Scholar]
  8. 8.  Bianconi G 2015. Europhys. Lett. 111:56001
     [Google Scholar]
  9. 9.  De Domenico M, Nicosia V, Arenas A, Latora V 2015. Nat. Commun. 6:6864
     [Google Scholar]
  10. 10.  Menichetti G, Remondini D, Panzarasa P, Mondragón RJ, Bianconi G 2014. PLOS ONE 9:e97857
     [Google Scholar]
  11. 11.  Kleineberg KK, Boguná M, Serrano MÁ, Papadopoulos F 2016. Nat. Phys. 12:1076
     [Google Scholar]
  12. 12.  Cozzo E, de Arruda GF, Rodrigues FA, Moreno Y 2016. See Reference 93 17–35
  13. 13.  Boccaletti S, Bianconi G, Criado R, Del Genio CI, Gómez-Gardenes J et al. 2014. Phys. Rep. 544:1–122
     [Google Scholar]
  14. 14.  Battiston F, Nicosia V, Latora V 2014. Phys. Rev. E 89:032804
     [Google Scholar]
  15. 15.  Aleta A, Meloni S, Moreno Y 2017. Sci. Rep. 7:44359
     [Google Scholar]
  16. 16.  Cozzo E, Kivelä M, De Domenico M, Solé-Ribalta A, Arenas A et al. 2015. New J. Phys. 17:073029
     [Google Scholar]
  17. 17.  de Arruda GF, Cozzo E, Moreno Y, Rodrigues FA 2016. Phys. D: Nonlinear Phenom. 323:5–11
     [Google Scholar]
  18. 18.  Nicosia V, Latora V 2015. Phys. Rev. E 92:032805
     [Google Scholar]
  19. 19.  Battiston F, Nicosia V, Latora V 2016. New J. Phys. 18:043035
     [Google Scholar]
  20. 20.  Solé-Ribalta A, De Domenico M, Gómez S, Arenas A 2016. Phys. D: Nonlinear Phenom. 323:73–79
     [Google Scholar]
  21. 21.  Tu X, Jiang GP, Song Y, Zhang X 2018. IEEE Access 6:12530–38
     [Google Scholar]
  22. 22.  Solé-Ribalta A, De Domenico M, Gómez S, Arenas A 2014. Proceedings of the 2014 ACM Conference on Web Science, Bloomington, IL, June 23–26149–55 New York: Assoc. Comput. Mach.
     [Google Scholar]
  23. 23.  Solá L, Romance M, Criado R, Flores J, García del Amo A, Boccaletti S 2013. Chaos: Interdiscip. J. Nonlinear Sci. 23:033131
     [Google Scholar]
  24. 24.  Buldú JM, Sevilla-Escoboza R, Aguirre J, Papo D, Gutiérrez R 2016. See Reference 93 61–77
  25. 25.  De Domenico M, Solé-Ribalta A, Omodei E, Gómez S, Arenas A 2015. Nat. Commun. 6:6868
     [Google Scholar]
  26. 26.  Reiffers-Masson A, Labatut V 2017. Netw. Sci. 5:213–34
     [Google Scholar]
  27. 27.  Cozzo E, Baños RA, Meloni S, Moreno Y 2013. Phys. Rev. E 88:050801
     [Google Scholar]
  28. 28.  Sánchez-García RJ, Cozzo E, Moreno Y 2014. Phys. Rev. E 89:052815
     [Google Scholar]
  29. 29.  Mucha PJ, Richardson T, Macon K, Porter MA, Onnela JP 2010. Science 328:876–78
     [Google Scholar]
  30. 30.  Pramanik S, Tackx R, Navelkar A, Guillaume JL, Mitra B 2017. 2017 IEEE International Conference on Data Science and Advanced Analytics (DSAA), Tokyo, Japan, Oct. 19–21611–20 Washington, DC: IEEE
     [Google Scholar]
  31. 31.  De Domenico M, Lancichinetti A, Arenas A, Rosvall M 2015. Phys. Rev. X 5:011027
     [Google Scholar]
  32. 32.  Jeub LGS, Mahoney MW, Mucha PJ, Porter MA 2017. Netw. Sci. 5:144–63
     [Google Scholar]
  33. 33.  Kuncheva Z, Montana G 2015. Proceedings of the 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, FAB 2015, FOSINT-SI 2015, NIBIBI 2015, Paris, France, Aug. 25–281308–15 New York: Assoc. Comput. Mach.
     [Google Scholar]
  34. 34.  Wilson JD, Palowitch J, Bhamidi S, Nobel AB 2017. J. Mach. Learn. Res. 18:5458–506
     [Google Scholar]
  35. 35.  Taylor D, Shai S, Stanley N, Mucha PJ 2016. Phys. Rev. Lett. 116:228301
     [Google Scholar]
  36. 36.  De Bacco C, Power EA, Larremore DB, Moore C 2017. Phys. Rev. E 95:042317
     [Google Scholar]
  37. 37.  Peixoto TP 2015. Phys. Rev. E 92:042807
     [Google Scholar]
  38. 38.  Vallès-Català T, Massucci FA, Guimerà R, Sales-Pardo M 2016. Phys. Rev. X 6:011036
     [Google Scholar]
  39. 39.  Lee KM, Min B, Goh KI 2015. Eur. Phys. J. B 88:48
     [Google Scholar]
  40. 40.  Schneider CM, Araújo NA, Herrmann HJ 2013. Phys. Rev. E 87:043302
     [Google Scholar]
  41. 41.  Hwang S, Choi S, Lee D, Kahng B 2015. Phys. Rev. E 91:022814
     [Google Scholar]
  42. 42.  Baxter G, Dorogovtsev S, Goltsev A, Mendes J 2012. Phys. Rev. Lett. 109:248701
     [Google Scholar]
  43. 43.  Danziger MM, Shekhtman LM, Bashan A, Berezin Y, Havlin S 2016. See Reference 93 79–99
  44. 44.  Huang X, Shao S, Wang H, Buldyrev SV, Stanley HE, Havlin S 2013. Europhys. Lett. 101:18002
     [Google Scholar]
  45. 45.  Shao S, Huang X, Stanley HE, Havlin S 2014. Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 89:032812
     [Google Scholar]
  46. 46.  Buldyrev SV, Parshani R, Paul G, Stanley HE, Havlin S 2010. Nature 464:1025
     [Google Scholar]
  47. 47.  Min B, Goh KI 2014. Phys. Rev. E 89:040802
     [Google Scholar]
  48. 48.  Shao J, Buldyrev SV, Havlin S, Stanley HE 2011. Phys. Rev. E 83:036116
     [Google Scholar]
  49. 49.  Son SW, Bizhani G, Christensen C, Grassberger P, Paczuski M 2012. Europhys. Lett. 97:16006
     [Google Scholar]
  50. 50.  Grassberger P 2015. Phys. Rev. E 91:062806
     [Google Scholar]
  51. 51.  Zhao Dw, Wang Lh, Zhi Y, Zhang J, Wang Z 2016. Sci. Rep. 6:24304
     [Google Scholar]
  52. 52.  Cellai D, Dorogovtsev SN, Bianconi G 2016. Phys. Rev. E 94:032301
     [Google Scholar]
  53. 53.  Min B, Do Yi S, Lee KM, Goh KI 2014. Phys. Rev. E 89:042811
     [Google Scholar]
  54. 54.  Lee KM, Goh KI 2016. Sci. Rep. 6:26346
     [Google Scholar]
  55. 55.  Reis SDS, Hu Y, Babino A, Andrade José S Jr., Canals S et al. 2014. Nat. Phys. 10:762–67
     [Google Scholar]
  56. 56.  Brummitt CD, Kobayashi T 2015. Phys. Rev. E 91:062813
     [Google Scholar]
  57. 57.  Baggio JA, BurnSilver SB, Arenas A, Magdanz JS, Kofinas GP, De Domenico M 2016. PNAS 113:13708–13
     [Google Scholar]
  58. 58.  De Domenico M, Granell C, Porter MA, Arenas A 2016. Nat. Phys. 12:901–6
     [Google Scholar]
  59. 59.  Amato R, Kouvaris NE, Miguel MS, Díaz-Guilera A 2017. New J. Phys. 19:123019
     [Google Scholar]
  60. 60.  Buono C, Alvarez-Zuzek LG, Macri PA, Braunstein LA 2014. PLOS ONE 9:e92200
     [Google Scholar]
  61. 61.  Gómez S, Arenas A, Borge-Holthoefer J, Meloni S, Moreno Y 2010. Europhys. Lett. 89:38009
     [Google Scholar]
  62. 62.  de Arruda GF, Cozzo E, Peixoto TP, Rodrigues FA, Moreno Y 2017. Phys. Rev. X 7:011014
     [Google Scholar]
  63. 63.  Valdano E, Ferreri L, Poletto C, Colizza V 2015. Phys. Rev. X 5:021005
     [Google Scholar]
  64. 64.  Min B, Gwak SH, Lee N, Goh KI 2016. Sci. Rep. 6:21392
     [Google Scholar]
  65. 65.  Zuzek LGA, Buono C, Braunstein LA 2015. J. Phys. Conf. Ser. 640:012007
     [Google Scholar]
  66. 66.  Kouvaris NE, Hata S, Guilera AD 2015. Sci. Rep. 5:10840
     [Google Scholar]
  67. 67.  Biondo AE, Pluchino A, Rapisarda A 2017. Ital. Econ. J. 3:343–66
     [Google Scholar]
  68. 68.  Nicosia V, Skardal PS, Arenas A, Latora V 2017. Phys. Rev. Lett. 118:138302
     [Google Scholar]
  69. 69.  Pilosof S, Porter MA, Pascual M, Kéfi S 2017. Nat. Ecol. Evol. 1:0101
     [Google Scholar]
  70. 70.  Finn KR, Silk MJ, Porter MA, Pinter-Wollman N 2017. arXiv:1712.01790
     [Google Scholar]
  71. 71.  Gosak M, Markovič R, Dolenšek J, Slak Rupnik M, Marhl M et al. 2018. Phys. Life Rev. 24:118–35
     [Google Scholar]
  72. 72.  Shinde P, Jalan S 2015. Europhys. Lett. 112:58001
     [Google Scholar]
  73. 73.  Zitnik M, Leskovec J 2017. Bioinformatics 33:i190–98
     [Google Scholar]
  74. 74.  Gallotti R, Barthelemy M 2015. Sci. Data 2:140056
     [Google Scholar]
  75. 75.  Gallotti R, Barthelemy M 2014. Sci. Rep. 4:6911
     [Google Scholar]
  76. 76.  Strano E, Shai S, Dobson S, Barthelemy M 2015. J. R. Soc. Interface 12:20150651
     [Google Scholar]
  77. 77.  Cardillo A, Zanin M, Gómez-Gardenes J, Romance M, del Amo AJG, Boccaletti S 2013. Eur. Phys. J. Spec. Top. 215:23–33
     [Google Scholar]
  78. 78.  Tsiotas D, Polyzos S 2015. J. Complex Netw. 3:642–70
     [Google Scholar]
  79. 79.  Hong C, Zhang J, Cao XB, Du WB 2016. Chaos, Solitons Fractals 86:28–34
     [Google Scholar]
  80. 80.  Jiang J, Zhang R, Guo L, Li W, Cai X 2016. Chin. Phys. Lett. 33:108901
     [Google Scholar]
  81. 81.  Betzel RF, Bassett DS 2017. NeuroImage 160:73–83
     [Google Scholar]
  82. 82.  De Domenico M 2017. Giga Sci. 6:1–8
     [Google Scholar]
  83. 83.  Battiston F, Nicosia V, Chavez M, Latora V 2017. Chaos: Interdiscip. J. Nonlinear Sci. 27:047404
     [Google Scholar]
  84. 84.  Musmeci N, Nicosia V, Aste T, Di Matteo T, Latora V 2017. Complexity 2017:
     [Google Scholar]
  85. 85.  Bargigli L, Di Iasio G, Infante L, Lillo F, Pierobon F 2015. Quant. Finance 15:673–91
     [Google Scholar]
  86. 86.  Zeng A, Battiston S 2016. PLOS ONE 11:e0158062
     [Google Scholar]
  87. 87.  Condorelli D, Galeotti A, Renou L 2016. Rev. Econ. Stud. 84:82–105
     [Google Scholar]
  88. 88.  Santana J, Hoover R, Vengadasubbu M 2017. Soc. Netw. 48:256–69
     [Google Scholar]
  89. 89.  Battiston S, Caldarelli G, D'Errico M 2016. See Reference 93 195–229
  90. 90.  Wang Z, Wang L, Szolnoki A, Perc M 2015. Eur. Phys. J. B 88:124
     [Google Scholar]
  91. 91.  Wang Z, Szolnoki A, Perc M 2013. Sci. Rep. 3:2470
     [Google Scholar]
  92. 92.  Battiston F, Perc M, Latora V 2017. New J. Phys. 19:073017
     [Google Scholar]
  93. 93.  Garas A 2016. Interconnected Networks Cham: Springer
     [Google Scholar]
/content/journals/10.1146/annurev-conmatphys-031218-013259
Loading
Multilayer Networks in a Nutshell
Annual Review of Condensed Matter Physics 10, 45 (2019); https://doi.org/10.1146/annurev-conmatphys-031218-013259
/content/journals/10.1146/annurev-conmatphys-031218-013259
/content/journals/10.1146/annurev-conmatphys-031218-013259
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error