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

ISBN-10: 3540403728

ISBN-13: 9783540403722

Networks delivers an invaluable version and image photograph precious for the outline of a wide number of web-like buildings within the actual and man-made realms, e.g. protein networks, meals webs and the web. The contributions accumulated within the current quantity offer either an creation to, and an outline of, the multifaceted phenomenology of complicated networks. Statistical Mechanics of advanced Networks also provides a cutting-edge photo of present theoretical equipment and techniques.

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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). 5. A. A. Simon: Models of Man (Wiley, New York, 1957). 6. -L. Barab´ asi, R. Albert: Science 286, 509 (1999); R. Albert, H. -L. Barab´ asi: Nature 401, 130 (1999). 7. U. Yule: Phil. Trans. Roy. Soc. B 213, 21 (1924); The Statistical Study of Literary Vocabulary (Cambridge University Press, Cambridge, 1944).

U=1−q+ q k ∞ kP (k)uk−1 . 19) to calculate the size of the inﬁnite cluster in a graph with a given degree distribution. 3 Critical Exponents Using Abelian and Tauberian methods [25, 26] one can use . 20) to ﬁnd the critical exponents for percolation in scale free networks. 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 and λ = 5. Bottom: shown (in diﬀerent colors) are shells of equidistant sites to the central one in a lattice of 300 x 300 sites. 5, shells are broken dmin . We will see that dmin < 1 (for d > 1), contrary to all naturally occurring fractals and disordered media. Sites at chemical distance l from a given site constitute its l-th chemical shell. The number of (connected) sites within radius r scales as m(r) ∼ rdf , deﬁning the fractal dimension df . Likewise, the number of (connected) sites within chemical radius l scales as m(l) ∼ ldl , which deﬁnes the fractal dimension dl in chemical space.

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

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