Abstract
In world wide web, a non-obvious but universal phenomenon called as peninsula phenomenon has been observed. The experiment results shows that the proportion f(x) of peninsulas with size x obey a power law distribution with exponent at least 1.913. In this paper we propose a stochastic model and prove theoretically that the size distribution of peninsulas have a stationary power law distribution with exponent 3+2a, where a>0. The numerical simulation results verify it too.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alon, N., Spencer, J.H.: The probablislic Method, 2nd edn. John Wiley and Sons, New York (2000)
Azuma, A.: Weighted sums of certain dependent variables. Tôhoku Math. J. 3, 357–367 (1967)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Bollobás, B., Riordan, O., Spencer, J., Tusnády, G.: The degree sequence of a scale-free random graph process. Random structures and Algorithms 18, 279–290 (2001)
Buckley, P.G., Osthus, D.: Popularity based random graph models leading to a scale-free degree sequence. Discrete Math. 282, 53–68 (2004)
Dorogovtsev, S.N., Mendes, J.F.F., Samukhin, A.N.: Structure of growing networks with preferential links. Phys. Rev. Lett. 85, 4633–4636 (2000)
Ma, Z.M.: Markovian random network processes. The jointed meeting of The Chinese Society and Statistics and the Institute of Mathematical Statictics, Beijing (2005)
Meng, J., Yan, H.F.: On the peninsula phenomenon in web graph and its implication on web search. Computer Networks 51, 177–189 (2007)
Kleinberg, J.M., Kumar, R., Raghavan, P., Rajagopalan, S., Tomkins, A.S.: The Web as a Graph: Measurements, Models, and Methods. In: Asano, T., Imai, H., Lee, D.T., Nakano, S.-i., Tokuyama, T. (eds.) COCOON 1999. LNCS, vol. 1627, p. 1. Springer, Heidelberg (1999), doi: 10.1.1.33.1635
Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., Upfal, E.: Stochastic models for the web graph. In: Proceedings of the 41th IEEE Symp. on Foundations of Computer Science, pp. 57–65 (2000)
Kumar, R., Raghavan, P., Rajagopalan, S., Tomkins, A., Upfal, E.: Trawling the web for emerging cyber-communities. Computer Networks 31, 1481–1493 (1999)
Zipf, G.K.: Human Behaviour and the Principle of Least Effort: An Introduction to Human Ecology. Addison-Wesley, Cambridge (1949)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag GmbH Berlin Heidelberg
About this chapter
Cite this chapter
Xiao, L., Ren, W., Yan, G. (2012). The Size Distribution of Peninsula in a Random Graph Process. In: Qian, Z., Cao, L., Su, W., Wang, T., Yang, H. (eds) Recent Advances in Computer Science and Information Engineering. Lecture Notes in Electrical Engineering, vol 127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25769-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-25769-8_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25768-1
Online ISBN: 978-3-642-25769-8
eBook Packages: EngineeringEngineering (R0)