Abstract
In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.
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References
Barabási, A. L., Albert, R.: Emergence of scaling in random networks. Science, 286, 509–512 (1999)
Solé, R. V., Paster-Satorras, R., Smith, E., et al.: A model of large-scale proteome evolution. Adv. Complex Syst., 5, 43–54 (2002)
Vazquez, A., Flammini, A., Maritan, A., et al.: Modeling of protein interaction networks. ComPlexUs, 1, 38–44 (2003)
Shi, D. H., Liu, L., Zhu, S. X., et al.: Degree distributions of evolving networks. Europhys. Lett., 76, 731–737 (2006)
Hou, Z. T., Kong, X. X., Shi, D. H., et al.: Degree-distribution stability of growing networks. Complex Sciences, 1827–1837 (2009)
Stolz, O.: Vorlesungen uber allgemiene Arithmetic, Teubner, Leipzig, 1886
Ye, B., Hou, Z. T., Kong, X. X.: Scale-free network with variable scaling exponent. International Workshop on Chaos-Fractals Theories and Applications, 400–403 (2010)
Albert, R., Barabási, A. L.: Topology of evolving networks: Local events and universality. Phys. Rev. Lett., 85, 5234–5237 (2000)
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Supported by National Natural Science Foundation of China (Grant No. 10901164), Graduate Research Innovation Projects in Hunan Province (Grant No. CX2009B020) and Graduate Degree Thesis Innovation Foundation of Central South University (Grant No. 2009ybfz11); the second author is supported by Natural Science Foundation of China (Grant Nos. 11071258, 90820302) and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090162110058)
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Kong, X.X., Hou, Z.T., Shi, D.H. et al. Markov chain-based degree distributions of evolving networks. Acta. Math. Sin.-English Ser. 28, 1981–1994 (2012). https://doi.org/10.1007/s10114-012-0054-y
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DOI: https://doi.org/10.1007/s10114-012-0054-y