Abstract
In this paper, we investigate networks grow in time according to an attachment rule that is random. Based on Markov chain theory, paper provides a rigorous proof for the existence of the steady-state degree distribution of the network generated by this model and gets its corresponding exact formulas. Moreover, we found this kind of networks don’t obey the power-law distribution.
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References
Bollobás, B.: The Grid: Modern Graph Theory. Springer, New York (1998)
Albert, R., Jeong, H., Barabási, A.-L.: The Diameter of the World-Wide Web. Nature 401, 130–131 (1999)
Newman, M.E.J.: Scientific collaboration networks. I. Network construction and fundamental results. Phys. Rev. E 64, 0161311–0161318 (2001)
Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of networks. Adv. Phys. 51, 1079–1187 (2002)
Bollobás, B., Riordan, O.: Mathematical results on scale-free random graphs. In: Handbook of Graphs and Networks, pp. 99–121. Wiley-VCH, Berlin (2002)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
Wagner, A.: The Yeast Protein Interaction Network Evolves Rapidly and Contains Few Redundant Duplicate Genes. Mol. Biol. Evol. 18, 1283–1292 (2001)
Wasserman, S., Faust, K.: Social network analysis: Methods and applications. Cambridge University Press, Cambridge (1994)
Garcia-Domingo, J.L., Juher, D., Saldanňa: Degree correlations in growing networks with deletion of nodes. Physica D 237, 640–651 (2008)
Barabási, A.-L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509–512 (1999)
Dorogovtsev, S.N., Mendes, J.F.F., Samukhin, A.N.: Structure of Growing Networks with Preferential Linking. Phys. Rev. Lett. 85, 4633–4636 (2000)
Krapivsky, P.L., Redner, S., Leyvraz, F.: Connectivity of Growing Random Networks. Phys. Rev. Lett. 85, 4629–4632 (2000)
Zhao, Q., et al.: The degree distribution of fixed act-size collaboration networks. Pramana-Journal of Physics 73, 955–959 (2009)
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Zhao, Q. (2012). The Degree Distribution of Random Attachment Networks. In: Jin, D., Lin, S. (eds) Advances in Electronic Commerce, Web Application and Communication. Advances in Intelligent and Soft Computing, vol 149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28658-2_44
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DOI: https://doi.org/10.1007/978-3-642-28658-2_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28657-5
Online ISBN: 978-3-642-28658-2
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