Degree distribution nearby the origin of a preferential attachment graph
Abstract
In a 2-parameter scale free model of random graphs it is shown that the asymptotic degree distribution is the same in the neighbourhood of every vertex. This degree distribution is still a power law with characteristic exponent 2, but this exponent is different from the one observed in the whole graph.
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Pages: 276-282
Publication Date: September 13, 2007
DOI: 10.1214/ECP.v12-1299
References
- Barabási, Albert-László; Albert, Réka. Emergence of scaling in random networks. Science 286 (1999), no. 5439, 509--512. MR2091634
- Cooper, Colin; Frieze, Alan. A general model of web graphs. Random Structures Algorithms 22 (2003), no. 3, 311--335. MR1966545
- Katona, Zsolt. Levels of a scale-free tree. Random Structures Algorithms 29 (2006), no. 2, 194--207. MR2245500
- Katona, Zsolt; Móri, Tamás F. A new class of scale free random graphs. Statist. Probab. Lett. 76 (2006), no. 15, 1587--1593. MR2248845
- Móri, T. F. On random trees. Studia Sci. Math. Hungar. 39 (2002), no. 1-2, 143--155. MR1909153
- Móri, Tamás F. A surprising property of the Barabási-Albert random tree. Studia Sci. Math. Hungar. 43 (2006), no. 2, 265--273. MR2229623
- Móri, T. F. On a 2-parameter class of scale free random graphs. Acta Math. Hungar. 114 (2007), no. 1-2, 37--48. MR2294512
- Neveu, J. Discrete-parameter martingales. Translated from the French by T. P. Speed. Revised edition. North-Holland Mathematical Library, Vol. 10. North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. viii+236 pp. MR0402915
- Szymański, Jerzy. On a nonuniform random recursive tree. Random graphs '85 (Poznań, 1985), 297--306, North-Holland Math. Stud., 144, North-Holland, Amsterdam, 1987. MR0930497

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