Paper Info
Title
Scale Free Properties Of Random K-Trees
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 onlymakes 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.
Year
DOI
Venue
2010
10.1007/s11786-010-0041-6
MATHEMATICS IN COMPUTER SCIENCE
Keywords
DocType
Volume
Scale free graph, Small world network, Clustering coefficient, k-Tree, Apollonian network
Journal
3
Issue
ISSN
Citations 
4
1661-8270
4
PageRank 
References 
Authors
0.47
2
2
Name
Order
Citations
PageRank
Colin Cooper185791.88
Ryuhei Uehara252875.38