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By Tomer Kalisky, Reuven Cohen, Daniel ben-Avraham, Shlomo Havlin (auth.), Eli Ben-Naim, Hans Frauenfelder, Zoltan Toroczkai (eds.)

This quantity is dedicated to purposes of the recommendations of statistical physics to the characterization and modeling of advanced networks. the 1st components of the publication drawback conception and modeling of networks, whereas the final elements survey functions to a wide selection of ordinary and synthetic networks. the educational reports that contain this booklet are meant for college kids and beginners to the sector, and so they represent a latest and entire reference for specialists. To this target, all contributions were conscientiously peer-reviewed not just for medical content material but in addition for self-consistency and clarity.

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Let H1 (x) be the generating function for the probability of reaching a branch of a given size by following a link. After a dilution of a fraction p of the sites (the remaining concentration is q = 1 − p), H1 (x) satisfies the self-consistent equation Tomography and Stability of Complex Networks 25 H1 (x) = 1 − q + qxG1 (H1 (x)) . (48) Since G0 (x) is the generating function for the degree of a site, the generating function for the probability of a site to belong to an n-site cluster is H0 (x) = 1 − q + qxG0 (H1 (x)) .

Shavitt, IEEE INFOCOM’03 (2003). 49. -I. Goh, B. Kahng and D. Kim, Phys. Rev. Lett. 87, 278701 (2001). 50. -I. Goh, E. Oh, H. Jeong, B. Kahng and D. Kim Proc. Natl. Acad. Sci. USA 99, 12583 (2002). 51. R. Pastor-Sattoras and A. Vespignani, Phys. Rev. E. 63, 066117 (2001). 52. R. Pastor-Satorras, and A. Vespignani Phys. Rev. E 65, 036104 (2002). 53. Z. -L. Barabasi, Phys. Rev. E 65, 055103 (R) (2002). 54. R. Cohen, D. ben-Avraham and S. Havlin, Phys. Rev. Lett. 91, 247901 (2003). Spectral Analysis of Random Networks Sergei N.

Vespignani, Phys. Rev. E. 63, 066117 (2001). 52. R. Pastor-Satorras, and A. Vespignani Phys. Rev. E 65, 036104 (2002). 53. Z. -L. Barabasi, Phys. Rev. E 65, 055103 (R) (2002). 54. R. Cohen, D. ben-Avraham and S. Havlin, Phys. Rev. Lett. 91, 247901 (2003). Spectral Analysis of Random Networks Sergei N. Dorogovtsev1,2 , Alexander V. F. Mendes2 , and Alexander N. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia Abstract. We review a general approach that describes the spectra of eigenvalues for random graphs with a local tree-like structure.

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