System Theory

Download Statistical Mechanics of Complex Networks (Lecture Notes in by Romualdo Pastor-Satorras, Miguel Rubi, Albert Diaz-Guilera PDF

By Romualdo Pastor-Satorras, Miguel Rubi, Albert Diaz-Guilera

Networks delivers an invaluable version and image photo necessary for the outline of a wide number of web-like buildings within the actual and man-made realms, e.g. protein networks, nutrients webs and the net. The contributions accrued within the current quantity supply either an creation to, and an outline of, the multifaceted phenomenology of complicated networks. Statistical Mechanics of complicated Networks also provides a state of the art photo of present theoretical tools and ways.

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Statistical Mechanics of Complex Networks (Lecture Notes in Physics)

Networks promises an invaluable version and photograph photograph invaluable for the outline of a wide number of web-like constructions within the actual and man-made realms, e. g. protein networks, foodstuff webs and the web. The contributions amassed within the current quantity supply either an advent to, and an outline of, the multifaceted phenomenology of complicated networks.

Extra resources for Statistical Mechanics of Complex Networks (Lecture Notes in Physics)

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Rajagopalan, A. Tomkins: in Lecture Notes in Computer Science, Vol. 1627 (Springer-Verlag, Berlin, 1999). 9. A. A. Adamic: Nature 401, 131 (1999); G. Caldarelli, R. Marchetti, L. Pietronero: Europhys. Lett. 52, 386 (2000) 10. A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins, J. Wiener: Computer Networks 33, 309 (2000). 11. L. M. : Nature 402, 83 (1999); A. J. : Nature 402, 86 (1999); T. : Proc. Natl. Acad. Sci. USA 97, 1143 (2000); ibid 98, 4569 (2001). 12. -C.

1 Random Scale-Free Networks The study of random network models began with Erd˝ os and R´enyi [1, 2, 3]. They studied models of networks with randomly distributed links. Those models lead to Poisson degree distributions [4]. Due to the development of computers, allowing the analysis of large amounts of data, and the formation of large scale networks, such as the Internet and WWW, some analysis of real world networks has been done in the last decade [5, 6, 7, 8, 9]. This research lead to the conclusion that real world networks are not described correctly by the ER model.

The work on protein networks was in collaboration with Byungnam Kahng and Jeenu Kim. This research was supported in part by NSF grant DMR9978902. References 1. H. Strogatz: Nature 410, 268 (2001); R. L. Barab´ asi: Rev. Mod. Phys. N. F. Mendes: Adv. Phys. 51, 1079 (2002). 2. H. Ernst: in Fractals in Physics, edited by L. Pietronero, E. Tosatti (Elsevier, Amsterdam, 1986), p. 289. 3. J. Bray: Adv. Phys. 43, 357 (1994). 4. A. Pimpinelli, J. Villain: Physics of Crystal Growth (Cambridge University Press, Cambridge, 1998).

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