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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/9177

Title: Scale free properties of random k-trees
Authors: Cooper, Colin
Uehara, Ryuhei
Keywords: Scale free graph
Small world network
Clustering coefficient
Apollonian network
Issue Date: 2010-04-16
Publisher: Springer
Magazine name: Mathematics in Computer Science
Volume: 3
Number: 4
Start page: 489
End page: 496
DOI: 10.1007/s11786-010-0041-6
Abstract: Scale free graphs have attracted attention as their non-uniform structure that can be used as a model for many social networks including the WWW and the Internet. In this paper, we propose a simple random model for generating scale free k-trees. For any fixed integer k, a k-tree consists of a generalized tree parameterized by k, and is one of the basic notions in the area of graph minors. Our model is quite simple and natural; it first picks a maximal clique of size k+1 uniformly at random, it then picks k vertices in the clique uniformly at random, and adds a new vertex incident to the k vertices. That is, the model only makes uniform random choices twice per vertex. Then (asymptotically) the distribution of vertex degree in the resultant k-tree follows a power law with exponent 2+1/k, the k-tree has a large clustering coefficient, and the diameter is small. Moreover, our experimental results indicate that the resultant k-trees have extremely small diameter, proportional to o(log n), where n is the number of vertices in the k-tree, and the o(1) term is a function of k.
Rights: This is the author-created version of Springer, Colin Cooper and Ryuhei Uehara, Mathematics in Computer Science, 3(4), 2010, 489-496. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/s11786-010-0041-6
URI: http://hdl.handle.net/10119/9177
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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