|
JAIST Repository >
b. 情報科学研究科・情報科学系 >
b10. 学術雑誌論文等 >
b10-1. 雑誌掲載論文 >
このアイテムの引用には次の識別子を使用してください:
http://hdl.handle.net/10119/9177
|
| タイトル: | Scale free properties of random k-trees |
| 著者: | Cooper, Colin
Uehara, Ryuhei |
| キーワード: | Scale free graph
Small world network
Clustering coefficient
k-Tree
Apollonian network |
| 発行日: | 2010-04-16 |
| 出版者: | Springer |
| 誌名: | Mathematics in Computer Science |
| 巻: | 3 |
| 号: | 4 |
| 開始ページ: | 489 |
| 終了ページ: | 496 |
| DOI: | 10.1007/s11786-010-0041-6 |
| 抄録: | 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 |
| 資料タイプ: | author |
| 出現コレクション: | b10-1. 雑誌掲載論文 (Journal Articles)
|
このアイテムのファイル:
| ファイル |
記述 |
サイズ | 形式 |
|---|
| 15048.pdf | | 134Kb | Adobe PDF | 見る/開く |
|
当システムに保管されているアイテムはすべて著作権により保護されています。
|
