Driving interconnected networks to supercriticality

Physical Review X

Volumn 4, Issue 2, 2014, Pages

  Radicchi, Filippo ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Complex systems; Interdisciplinary physics; Statistical physics

Indexed keywords

LARGE SCALE SYSTEMS; NETWORK LAYERS;

COMPLICATED STRUCTURES; DEGREE DISTRIBUTIONS; DYNAMICAL BEHAVIORS; INTERCONNECTED NETWORK; INTERDISCIPLINARY PHYSICS; MUTUAL DEPENDENCES; STATISTICAL PHYSICS; SUPERCRITICAL REGIME;

TOPOLOGY;

EID: 84901293148     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.4.021014     Document Type: Article

References (31)

1. S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, Catastrophic Cascade of Failures in Interdependent Networks, Nature (London) 464, 1025 (2010).
2. M. Szell, R. Lambiotte, and S. Thurner, Multirelational Organization of Large-Scale Social Networks in an Online World, Proc. Natl. Acad. Sci. U.S.A. 107, 13 636 (2010).
3. M. Barthélemy, Spatial Networks, Phys. Rep. 499, 1 (2011).
4. F. Radicchi and A. Arenas, Abrupt Transition in the Structural Formation of Interconnected Networks, Nat. Phys. 9, 717 (2013).
5. S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Critical Phenomena in Complex Networks, Rev. Mod. Phys. 80, 1275 (2008).
6. R. Parshani, S. V. Buldyrev, and S. Havlin, Interdependent Networks: Reducing the Coupling Strength Leads to a Change from a First to Second Order Percolation Transition, Phys. Rev. Lett. 105, 048701 (2010).
7. J. Gao, S. V. Buldyrev, S. Havlin, and H. E. Stanley, Robustness of a Network of Networks, Phys. Rev. Lett. 107, 195701 (2011).
8. J. Gao, S. V. Buldyrev, H. E. Stanley, and S. Havlin, Networks Formed from Interdependent Networks, Nat. Phys. 8, 40 (2012).
9. S.-W. Son, G. Bizhani, C. Christensen, P. Grassberger, and M. Paczuski, Percolation Theory on Interdependent Networks Based on Epidemic Spreading, Europhys. Lett. 97, 16 006 (2012).
10. F. Chung, Spectral Graph Theory (American Mathematical Society, 1996).
11. S. Jianbo and M. Jitendra, Normalized Cuts and Image Segmentation, IEEE Trans. Pattern Anal. Mach. Intell. 22, 888 (1997).
12. M. Rosvall and C. T. Bergstrom, Maps of Random Walks on Complex Networks Reveal Community Structure, Proc. Natl. Acad. Sci. U.S.A. 105, 1118 (2008).
13. M. Cavers, S. Fallat, and S. Kirkland, On the Normalized Laplacian Energy and General Randic Index R-1 of Graphs, Linear Algebra Appl. 433, 172 (2010).
14. P. G. Doyle and L. Snell, Random Walks and Electric Networks (Mathematical Association of America, Washington, D.C., 1984).
15. D. J. Klein and M. Randic, Resistance Distance, J. Math. Chem. 12, 81 (1993).
16. H. C. Berg, Random Walks in Biology (Princeton University Press, Princeton, NJ, 1993).
17. S. Brin and L. Page, The Anatomy of a Large-Scale Hypertextual Web Search Engine, Comput. Netw. ISDN Syst. 30, 107 (1998).
18. E. A. Codling, M. J. Plank, and S. Benhamou, Random Walk Models in Biology, J. R. Soc. Interface 5, 813 (2008).
19. B. G. Malkiel, A Random Walk Down Wall Street (Norton, New York, 1973).
20. G. H. Weiss, Aspects and Applications of the Random Walk (Random Materials and Processes) (North-Holland, Amsterdam, 1994).
21. M. Faccin, T. Johnson, J. Biamonte, S. Kais, and P. Migdal, Degree Distribution in Quantum Walks on Complex Networks, Phys. Rev. X 3, 041007 (2013).
22. L. Lovász, in Combinatorics, Paul Erdos is Eighty, edited by D. Miklós, V. T. Sós, and T. Szonyi (János Bolyai Mathematical Society, Budapest, Hungary, 1996), Vol. 2, p. 1-46.
23. I. B. Schwartz and L. Billings, Fluctuations Induced Almost Invariant Sets, Naval Research Laboratory Technical Report No. NRL-MR-6790-06-9012, 2006.
24. S. Fortunato, Community Detection in Graphs, Phys. Rep. 486, 75 (2010).
25. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevX.4.021014 for explicit calculations and additional figures.
26. S. Blundell and K. M. Blundell, Concepts in Thermal Physics (Oxford University Press, New York, 2006).
27. F. Chung, L. Lu, and V. Vu, Spectra of Random Graphs with Given Expected Degrees, Proc. Natl. Acad. Sci. U.S.A. 100, 6313 (2003).
28. J. von Neumann and E. Wigner, No Crossing Rule, Z. Phys. 30, 467 (1929).
29. P. D. Lax, Linear Algebra and Its Applications (Wiley-Interscience, New York, 2007), 2nd ed.
30. Z. Darczy, Rearrangement Inequalities, Publ. Math. Debrecen 20, 273 (1973).
31. M. McHugh and V. Krukonis, Supercritical Fluid Extraction: Principles and Practice (Butterworth-Heinemann, London, 1986).