Read e-book online Statistical mechanics of complex networks PDF

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

ISBN-10: 3540403728

ISBN-13: 9783540403722

Networks provides an invaluable version and image photograph beneficial for the outline of a large choice of web-like constructions within the actual and man-made nation-states, e.g. protein networks, nutrition webs and the web. The contributions collected within the current quantity supply either an creation to, and an outline of, the multifaceted phenomenology of complicated networks. Statistical Mechanics of advanced Networks additionally offers a state of the art photograph of present theoretical tools and methods.

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Vespignani: cond-mat/0108043. V. Sol´e, R. Pastor-Satorras, E. D. Smith, T. Kepler: Adv. Complex Syst. 5, 43 (2002); R. D. V. Sol´e: preprint. J. L. Krapivsky, B. Kahng, S. Redner: Phys. Rev. E 66, 055101 (2002). J. Berg, M. L¨ assig, A. Wagner: cond-mat/0207711. L. Krapivsky, S. Redner, F. Leyvraz: Phys. Rev. Lett. 85, 4629 (2000). N. F. N. Samukhin: Phys. Rev. Lett. 85, 4633 (2000). L. Krapivsky, S. Redner: Phys. Rev. E 63, 066123 (2001). N. F. Mendes, A. N. Samukhin: Phys. Rev. E 64, 066110 (2001).

Some preliminary results can be found in [27]. A more detailed treatment can be found in [28, 19]. Here we just state the results. 21) 3 < λ < 4,   1 λ > 4. The number of clusters with size s behaves as ns ∼ (p − pc )−τ , where τ =2+ 1 2λ − 3 = , λ−2 λ−2 2<λ<4. 5, which is the regular mean field value. From those results it can be seen that the critical exponents are anomalous even when the second moment k 2 is convergent and only the third moment k 3 diverges, as in the case of 3 < λ < 4. From τ it can be deduced that the “double jump” in Erd˝ os-R´enyi graphs is also seen in scale free graphs, Where S, the size of largest component, scales as S ∼ N (λ−2)/(λ−1) exactly at criticality [19].

Phys. A 35 9517 (2002). J. E. , Malabar, 1987). H. C. Manrubia: Physica A 295, 1 (2001). L. Kullmann, J. Kert´esz: Phys. Rev. E 63, 051112 (2001); D. Lancaster: J. Phys. A 35, 1179 (2002). Z. D. Correia, A. Krzywicki: Phys. Rev. E 64, 046118 (2001). L. Krapivsky, S. Redner: Phys. Rev. Lett. xx xxxx (2002). A. S. N. Amaral: cond-mat/0205411. L. E. Knuth, O. : Addison-Wesley, 1989). L. Krapivsky, S. Redner: Computer Networks 39, 261 (2002). S. E. M. J. H. Strogatz: Phys. Rev. E 64, 041902 (2001).

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Statistical mechanics of complex networks by Romualdo Pastor-Satorras, Miguel Rubi, Albert Diaz-Guilera


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