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Albert R., BarabАsi A.-L. Statistical Mechanics of Complex Networks // Rev. Mod. Phys. -- 2002. -- Vol. 74. -- P. 4397. Bianconi G., BarabАsi A.-L. Competition and multiscaling in evolving networks // Europhys. Lett. -- 2001. -- Vol. 54. -- P. 436442. Boccaletti S., Latora V. et al. Complex networks: Structure and dynamics // Physics Repor. -- 2006. -- Vol. 424. -- P. 175308. Caldarelli G. Scale-Free Networks: Complex Webs in Nature and Technology -- Oxford: Oxford University Press, 2007. -- P. 272. Dorogovtsev S.N., Mendes J.F.F. Evolution of networks // Adv. Phys. -- 2002. -- Vol. 51. -- P. 10791187. Dorogovtsev S.N., Mendes J.F.F. Evolution of networks with aging of sites // Phys. Rev. E. -- 2000. -- Vol. 62. -- P. 18421845. Li X., Chen G. A local-world evolving network model // Physica A. -- 2003. -- Vol. 328. -- P. 274286.

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5. Part 5. Mathematical Theories and Calculation Methods

EFFECT OF AGING ON A LOCAL-WORLD NETWORK WITH COMPETITION Gadjiev B. R., Progulova T. B., Shchetinina D. P.

We present an algorithm for generation of local-world networks with nodes' competition that is a generalization of the local-world evolving network model. We generated such networks for different distributions of fitness parameters and showed that changing distribution of fitness parameter strongly alters network topology. Besides, we demonstrate that in cases of homogeneous and power-law distributions of the fitness parameter network alters from assortative to non-correlated and then to disassortative. For these cases we studied network resistance to random-type failures and targeted attacks.

98