Download Networks of Networks: The Last Frontier of Complexity by Gregorio D'Agostino, Antonio Scala PDF

By Gregorio D'Agostino, Antonio Scala

The current paintings is intended as a connection with offer an natural and complete view of the main correct ends up in the fascinating new box of Networks of Networks (NetoNets). Seminal papers have lately been released posing the foundation to review what occurs while varied networks have interaction, therefore supplying proof for the emergence of latest, unforeseen behaviors and vulnerabilities. From these seminal works, the notice at the significance figuring out Networks of Networks (NetoNets) has unfold to the whole neighborhood of Complexity technological know-how. The reader will enjoy the event of a few of the main well-recognized leaders during this box. The contents were aggregated lower than 4 headings; basic concept, Phenomenology, functions and danger evaluate. The reader might be inspired by way of the several purposes of the final paradigm that span from body structure, to monetary danger, to transports. we're at present making the 1st steps to minimize the space among the language and how of taking into consideration the 2 groups of specialists in genuine infrastructures and the complexity scientists. even though this course could turn out to be lengthy, this can be very promising, either in extending our knowing of complicated platforms and to find concrete functions which may increase the lifestyles caliber of thousands of individuals.

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Summer, Management science 52(9), 1301 (2006) E. Nier, J. Yang, T. Yorulmazer, A. Alentorn, Journal of Economic Dynamics and Control 31(6), 2033 (2007) R. Cifuentes, G. S. Shin, Journal of the European Economic Association 3(2–3), 556 (2005) I. A. J. S. Corner, Central Banker (Fall) (2011) Y. G. R. L. Q. M. K. Liu, T. , Physical Review E 84(2), 026101 (2011) A. P. W. Kantelhardt, S. C. J. M. Evans, J. F. C. Schultz, N. Marwan, Y. Zou, J. Kurths, The European Physical Journal B 84(4), 635 (2011) M.

If A p (k) is the number of nodes with degree k and Pp (k) the new degree distribution of the remaining fraction p of nodes in network A, then 1 Network of Interdependent Networks Pp (k) = 23 A p (k) . 38) where k( p)α ≡ Pp (k)k α . In the limit of N → ∞, Eq. 38) can be presented in terms of a derivative of A p (k) with respect to p, Pp (k)k α d A p (k) =N . 39) Differentiating Eq. 37) with respect to p and using Eq. 40) which is exact for N → ∞. In order to solve Eq. 40), we define a function α G α (x) ≡ k P(k)x k , and substitute f ≡ G −1 α ( p).

Kenett et al. where µ0 = p and µn are intermediate variables that satisfy µn = pgA (µn−1 ), n is odd, µn = pgB (µn−1 ), n is even. 49) As interdependent networks A and B form a stable mutually-connected giant component, n → ∞ and µn = µn−2 , the fraction of nodes left in the giant component is p∞ . 50) y = pgB (x), where the two unknown variables x and y can be used to calculate p∞ = xgB (x) = ygA (y). 51) x = pgA [ pgB (x)]. 52) 1 = p2 dx dx which, together with Eq. 51), yields the solution for pc and the critical size of the giant mutually-connected component, p∞ ( pc ) = xc gB (xc ).

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