Resilience of networks with community structure behaves as if under an external field

Proceedings of the National Academy of Sciences of the United States of America

Volumn 115, Issue 27, 2018, Pages 6911-6915

  Dong, Gaogao ^a,b,c   Fan, Jingfang ^d   Shekhtman, Louis M ^d   Shai, Saray ^e   Du, Ruijin ^a,b,c   Tian, Lixin ^a,f   Chen, Xiaosong ^g,h   Eugene Stanley, H ^b,c,i   Havlin, Shlomo ^d,i  

^a JIANGSU UNIVERSITY   (China)

^b BOSTON UNIVERSITY   (United States)

^c USA   (United States)

^d BAR ILAN UNIVERSITY   (Israel)

^e WESLEYAN UNIVERSITY   (United States)

^f NANJING NORMAL UNIVERSITY   (China)

^g UNIVERSITY OF CHINESE ACADEMY OF SCIENCES   (China)

^h INSTITUTE OF THEORETICAL PHYSICS   (China)

ⁱ TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Community structure; External field; Percolation; Resilience; Universality

Indexed keywords

FERROMAGNETIC MATERIAL;

ARTICLE; ARTIFICIAL NEURAL NETWORK; COMMUNITY STRUCTURE; CONCEPTUAL FRAMEWORK; CONTROLLED STUDY; MATHEMATICAL MODEL; METHODOLOGY; PERCOLATION THEORY; PHASE TRANSITION; PRIORITY JOURNAL; RESILIENCE OF NETWORKS; STATISTICAL ANALYSIS; THEORY;

EID: 85049381363     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1801588115     Document Type: Article

References (61)

1. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442.
2. Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512.
3. Cohen R, Havlin S (2010) Complex Networks: Structure, Robustness and Function (Cambridge Univ Press, New York).
4. Newman MEJ (2010) Networks: An Introduction (Oxford Univ Press, Oxford).
5. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: Structure and dynamics. Phys Rep 424:175–308.
6. Fan J, Meng J, Ashkenazy Y, Havlin S, Schellnhuber HJ (2017) Network analysis reveals strongly localized impacts of El Niño. Proc Natl Acad Sci USA 114:7543–7548.
7. Boers N, et al. (2014) Prediction of extreme floods in the eastern central Andes based on a complex networks approach. Nat Commun 5:5199.
8. Cohen R, Erez K, Ben-Avraham D, Havlin S (2000) Resilience of the internet to random breakdowns. Phys Rev Lett 85:4626–4628.
9. Gao J, Barzel B, Barabási AL (2016) Universal resilience patterns in complex networks. Nature 530:307–312.
10. Sokolov I (1986) Dimensionalities and other geometric critical exponents in percolation theory. Physics-Uspekhi 29:924–945.
11. Coniglio A (1982) Cluster structure near the percolation threshold. J Phys A: Math Gen 15:3829–3844.
12. Coniglio A, Nappi CR, Peruggi F, Russo L (1977) Percolation points and critical point in the Ising model. J Phys A: Math Gen 10:205–218.
13. Stauffer D, Aharony A (1994) Introduction to Percolation Theory (Taylor and Francis, London).
14. Bunde A, Havlin S (2012) Fractals and Disordered Systems (Springer Science & Business Media, Berlin).
15. Saberi AA (2015) Recent advances in percolation theory and its applications. Phys Rep 578:1–32.
16. Dorogovtsev S, Goltsev A, Mendes J (2008) Critical phenomena in complex networks. Rev Mod Phys 80:1275–1335.
17. Dorogovtsev SN, Goltsev AV, Mendes JFF (2006) K-core organization of complex networks. Phys Rev Lett 96:040601.
18. Liu YY, Csóka E, Zhou H, Pósfai M (2012) Core percolation on complex networks. Phys Rev Lett 109:205703.
19. Newman MEJ, Strogatz SH, Watts DJ (2001) Random graphs with arbitrary degree distributions and their applications. Phys Rev E 64:026118.
20. Brockmann D, Helbing D (2013) The hidden geometry of complex, network-driven contagion phenomena. Science 342:1337–1342.
21. Hufnagel L, Brockmann D, Geisel T (2004) Forecast and control of epidemics in a globalized world. Proc Natl Acad Sci USA 101:15124–15129.
22. Dorogovtsev SN, Goltsev AV, Mendes JFF (2002) Ising model on networks with an arbitrary distribution of connections. Phys Rev E 66:016104.
23. Bollobás B (2001) Random Graphs (Cambridge Univ Press, Cambridge, UK).
24. Achlioptas D, D’souza RM, Spencer J (2009) Explosive percolation in random networks. Science 323:1453–1455.
25. Riordan O, Warnke L (2011) Explosive percolation is continuous. Science 333:322–324.
26. Cho YS, Hwang S, Herrmann HJ, Kahng B (2013) Avoiding a spanning cluster in percolation models. Science 339:1185–1187.
27. Buldyrev SV, Parshani R, Paul G, Stanley HE, Havlin S (2010) Catastrophic cascade of failures in interdependent networks. Nature 464:1025–1028.
28. Gao J, Buldyrev SV, Stanley HE, Havlin S (2012) Networks formed from interdependent networks. Nat Phys 8:40–48.
29. Yuan X, Hu Y, Stanley HE, Havlin S (2017) Eradicating catastrophic collapse in interdependent networks via reinforced nodes. Proc Natl Acad Sci USA 114:3311–3315.
30. Kivelä M, et al. (2014) Multilayer networks. J Complex Netw 2:203–271.
31. Boccaletti S, et al. (2014) The structure and dynamics of multilayer networks. Phys Rep 544:1–122.
32. Shekhtman LM, Danziger MM, Havlin S (2016) Recent advances on failure and recovery in networks of networks. Chaos, Solit Fractals 90:28–36.
33. Reis SDS, et al. (2014) Avoiding catastrophic failure in correlated networks of networks. Nat Phys 10:762–767.
34. Gao J, Liu X, Li D, Havlin S (2015) Recent progress on the resilience of complex networks. Energies 8:12187–12210.
35. Leicht EA, D’Souza RM (2009) Percolation on interacting networks. arXiv:0907.0894.
36. Wang H, et al. (2013) Effect of the interconnected network structure on the epidemic threshold. Phys Rev E 88:022801.
37. Radicchi F, Arenas A (2013) Abrupt transition in the structural formation of interconnected networks. Nat Phys 9:717–720.
38. Meunier D, Lambiotte R, Bullmore ET (2010) Modular and hierarchically modular organization of brain networks. Front Neurosci 4:200.
39. Stam CJ, Hillebrand A, Wang H, Van Mieghem P (2010) Emergence of modular structure in a large-scale brain network with interactions between dynamics and connectivity. Front Comput Neurosci 4:133.
40. Morone F, Roth K, Min B, Stanley HE, Makse HA (2017) Model of brain activation predicts the neural collective influence map of the brain. Proc Natl Acad Sci USA 114:3849–3854.
41. Guimerà R, Mossa S, Turtschi A, Amaral LAN (2005) The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles. Proc Natl Acad Sci USA 102:7794–7799.
42. Eriksen KA, Simonsen I, Maslov S, Sneppen K (2003) Modularity and extreme edges of the internet. Phys Rev Lett 90:148701.
43. Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99:7821–7826.
44. Liu D, Blenn N, Van Mieghem P (2012) A social network model exhibiting tunable overlapping community structure. Proced Computer Sci 9:1400–1409.
45. Thiemann C, Theis F, Grady D, Brune R, Brockmann D (2010) The structure of borders in a small world. PLoS One 5:e15422.
46. Lancichinetti A, Fortunato S, Kertész J (2009) Detecting the overlapping and hierarchical community structure in complex networks. New J Phys 11:033015.
47. Onnela JP, et al. (2007) Structure and tie strengths in mobile communication networks. Proc Natl Acad Sci USA 104:7332–7336.
48. González MC, Herrmann HJ, Kertész J, Vicsek T (2007) Community structure and ethnic preferences in school friendship networks. Physica A 379:307–316.
49. Mucha PJ, Richardson T, Macon K, Porter MA, Onnela JP (2010) Community structure in time-dependent, multiscale, and multiplex networks. Science 328:876–878.
50. Gladwell M (2006) The Tipping Point: How Little Things Can Make a Big Difference (Little, Brown, New York).
51. Stanley HE (1971) Phase Transitions and Critical Phenomena (Clarendon, Oxford).
52. Huang K (2009) Introduction to Statistical Physics (CRC, Boca Raton, FL).
53. Reynolds PJ, Stanley HE, Klein W (1977) Ghost fields, pair connectedness, and scaling: Exact results in one-dimensional percolation. J Phys A: Math Gen 10:L203–L209.
54. Erdos P, Rényi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5:17–60.
55. Cohen R, Ben-Avraham D, Havlin S (2002) Percolation critical exponents in scale-free networks. Phys Rev E 66:036113.
56. Domb C (2000) Phase Transitions and Critical Phenomena (Academic, New York), Vol 19.
57. Yang J, Leskovec J (2015) Defining and evaluating network communities based on ground-truth. Knowl Inf Syst 42:181–213.
58. Rossi RA, Ahmed NK (2015) The network data repository with interactive graph analytics and visualization. Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence (AAAI, Menlo Park, CA), 4292–4293.
59. Castellano C, Pastor-Satorras R (2017) Relating topological determinants of complex networks to their spectral properties: Structural and dynamical effects. Phys Rev X 7:041024.
60. Radicchi F, Castellano C (2015) Breaking of the site-bond percolation universality in networks. Nat Commun 6:10196.
61. Clauset A, Newman MEJ, Moore C (2004) Finding community structure in very large networks. Phys Rev E 70:066111.