Lack of spectral gap and hyperbolicity in asymptotic Erdos-Renyi sparse random graphs

5th International Symposium on Communications Control and Signal Processing, ISCCSP 2012

Volumn , Issue , 2012, Pages

  Narayan, Onuttom ^a   Saniee, Iraj ^b   Tucci, Gabriel H ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

Cheeger Constant; Hyperbolic Networks; Random Graphs; Spectral Gap

Indexed keywords

CHEEGER CONSTANT; HYPERBOLICITY; NORMALIZED LAPLACIAN; POSITIVE PROBABILITY; RANDOM GRAPHS; SPECTRAL GAP;

SIGNAL PROCESSING;

GRAPH THEORY;

EID: 84864114924     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISCCSP.2012.6217860     Document Type: Conference Paper

References (19)

1. P. Erd̈os and A. Renyi, Random Graphs I, Publ. Math. Inst. Hungar. Acad. Sci. 6, pp. 290-297, 1959.
2. E. Gilbert, Random Graphs, Annals of Mathematical Statistics, vol. 30, no. 4, pp. 1141-1144, 1959.
3. F. Chung, Spectral Graph Theory, CBMS Number 92, AMS, 1994.
4. A. Coja-Oghlan, A. Lanka, The spectral gap of random graphs with given expected degrees, The Elect. Journal of Combinatorics, 16, 2009.
5. E. A. Jonckheere, P. Lohsoonthorn, Geometry of network security, Proc. of the American Control Conf., 2004.
6. F. Chung, L. Liu, V. Vu, Spectra of random graphs with given expected degrees, PNAS vol. 100, no. 11, pp. 6313-6318, 2007.
7. M. Gromov, Hyperbolic Groups, Essays in group theory, Springer, New York, pp. 75-263, 1987.
8. M. Brisdon, A. Haefliger, Metric spaces of non-positive curvature, Springer Verlag, vol. 319, 1991.
9. A. Samukhin, S. Dorogovtsev and J. Mendes, Laplacian spectra of, and random walks on, complex networks: Are scale-free architectures really important, Phys. Rev. 77, 036115, 2008.
10. B. McKay, The Expected Eigenvalue Distribution of a Large Regular Graph, Lin. Alg. and Applications, vol. 40, pp. 203-216, 1981.
11. R. Lyons and Y. Peres, Probability on Trees and Networks, Course Notes, Fall 2004 (forthcoming book), http://php.indiana.edu/rdlyons/prbtree/prbtree. html, 2004.
12. C. Bordenave, M. Lelarge, Resolvent of Large Random Graphs, to appear in Random Structures and Algorithms, http://arxiv.org/0801.0155.
13. B. Mohar, The Laplacian Spectrum of Graphs, Graph Theory, Combinatorics, and Appl., vol. 2, pp. 871-898, 1991.
14. L. He, X. Liu and G. Strang, Trees with Cantor Eigenvalue Distribution, Studies in Appl. Math. vol. 110, pp. 123-136, 2003.
15. M. Mezard, A. Montanari, Information, Physics and Computation, Oxford University Press, 2009.
16. B. Karrer and M.E. Newman, Random graphs containing arbitrary distribution of sub-graphs, http://arxiv.org/1005.1659.
17. O. Narayan, I. Saniee, The large scale curvature of networks, http://arxiv.org/0907.1478.
18. O. Narayan, I. Saniee, G. Tucci, Lack of Spectral Gap and Hyperbolicity in Asymptotic Erd̈os-Renyi Random Graphs, http://arxiv.org/abs/1009.5700.
19. Z. F̈uredi and J. Komlos, The eigenvalues of random symmetric matrices, Combinatoria 1:3, pp. 233-241, 1981.