Degree Distribution of a Mixed Attachments Model for Evolving Networks

  • Lei Min
  • Zhao Qinggui
Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 117)


In this paper, we propose and investigate a evolving network model with both preferential and random attachment of new links, incorporating the additions of new nodes, new links, and the removals of links. 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 and show that the model can generate scale-free evolving network.


Mixed attachment Evolving network Scale-free Markov chain Degree distribution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Albert, R., Jeong, H., Barabási, A.-L.: The Diameter of the World-Wide Web. Nature 401, 130–131 (1999)CrossRefGoogle Scholar
  2. 2.
    Newman, M.E.J.: Scientific collaboration networks. I. Network construction and fundamental results. Phys. Rev. E 64, 0161311–0161318 (2001)Google Scholar
  3. 3.
    Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)zbMATHCrossRefGoogle Scholar
  4. 4.
    Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of networks. Adv. Phys. 51, 1079–1187 (2002)CrossRefGoogle Scholar
  5. 5.
    Bollobás, B., Riordan, O.: Mathematical results on scale-free random graphs. In: Handbook of Graphs and Networks, pp. 99–121. Wiley-VCH, Berlin (2002)Google Scholar
  6. 6.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar
  7. 7.
    Wagner, A.: The Yeast Protein Interaction Network Evolves Rapidly and Contains Few Redundant Duplicate Genes. Mol. Biol. Evol. 18, 1283–1292 (2001)CrossRefGoogle Scholar
  8. 8.
    Wasserman, S., Faust, K.: Social network analysis: Methods and applications. Cambridge University Press, Cambridge (1994)Google Scholar
  9. 9.
    Garcia-Domingo, J.L., Juher, D., Saldanňa: Degree correlations in growing networks with deletion of nodes. Physica D 237, 640–651 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Krapivsky, P.L., Redner, S., Leyvraz, F.: Connectivity of Growing Random Networks. Phys. Rev. Lett. 85, 4629–4632 (2000)CrossRefGoogle Scholar
  11. 11.
    Shi, D., Chen, Q.H., Liu, L.M.: Degree distributions of evolving networks. Europhys. Lett. 76, 731–737 (2006)CrossRefGoogle Scholar
  12. 12.
    Liu, Z., Lai, Y.-C., et al.: Connectivity distribution and attack tolerance of general networks with both preferential and random attachments. Physics Letters A 303, 337–344 (2002)zbMATHCrossRefGoogle Scholar
  13. 13.
    Zhao, Q., et al.: The degree distribution of fixed act-size collaboration networks. Pramana-Journal of Physics 73, 955–959 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.School of MathematicsCentral South University, CSUChangshaChina
  2. 2.College of Electrical and Information EngineeringHunan University of TechnologyZhuzhouChina
  3. 3.School of Mathematics and StatisticsChongqing University of Arts and Sciences, CUASChongqingChina

Personalised recommendations