Abstract
The World Wide Web may be viewed as a graph each of whose vertices corresponds to a static HTML web page, and each of whose edges corresponds to a hyperlink from one web page to another. Recently there has been considerable interest in using random graphs to model complex real-world networks to gain an insight into their properties. In this paper, we propose a generalized version of the protean graph (a random model of the web graph) in which the degree of a vertex depends on its age. Classic protean graphs can be seen as a special case of the rank-based approach where vertices are ranked according to age. Here, we investigate graph generation models based on other ranking schemes and show that these models lead to graphs with a power law degree distribution.
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References
Bonato, A.: A survey of web graph models. In: Proceedings of Combinatorial and Algorithm Aspects of Networking (2004)
Broder, A., Kumar, R., Maghoul, F., Rahaghavan, P., Rajagopalan, S., State, R., Tomkins, A., Wiener, J.: Graph structure in the web. In: Proc. 9th International World-Wide Web Conference (WWW), pp. 309–320 (2000)
Fortunato, S., Flammini, A., Menczer, F.: Scale-free network growth by ranking. Phys. Rev. Lett. 96(21), 218701 (2006)
Janson, S., Łuczak, T., Ruciński, A.: Random Graphs. Wiley, Chichester (2000)
Janssen, J., Prałat, P.: Rank-based attachment leads to power law graphs (preprint)
Łuczak, T., Prałat, P.: Protean graphs. Internet Mathematics 3, 21–40 (2006)
Pittel, B., Spencer, J., Wormald, N.: Sudden emergence of a giant k-core in a random graph. J. Combinatorial Theory Series B 67, 111–151 (1996)
Prałat, P.: A note on the diameter of protean graphs. Discrete Mathematics 308, 3399–3406 (2008)
Prałat, P., Wormald, N.: Growing protean graphs. Internet Mathematics, 13 (accepted)
Wormald, N.C.: Random graphs and asymptotics. Section 8.2. In: Gross, J.L., Yellen, J. (eds.) Handbook of Graph Theory, pp. 817–836. CRC, Boca Raton (2004)
Wormald, N.: The differential equation method for random graph processes and greedy algorithms. In: Karoński, M., Prömel, H.J. (eds.) Lectures on Approximation and Randomized Algorithms, pp. 73–155. PWN, Warsaw (1999)
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Prałat, P. (2008). Protean Graphs with a Variety of Ranking Schemes. In: Yang, B., Du, DZ., Wang, C.A. (eds) Combinatorial Optimization and Applications. COCOA 2008. Lecture Notes in Computer Science, vol 5165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85097-7_14
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DOI: https://doi.org/10.1007/978-3-540-85097-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85096-0
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