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| the small-community phenomenon in networks | |
| Li Angsheng; Peng Pan | |
| 2012 | |
| Source | Mathematical Structures in Computer Science
 |
| ISSN | 0960-1295 |
| Volume | 22Issue:3Pages:373-407 |
| English Abstract | We investigate several geometric models of networks that simultaneously have some nice global properties, including the small-diameter property, the small-community phenomenon, which is defined to capture the common experience that (almost) everyone in society also belongs to some meaningful small communities, and the power law degree distribution, for which our result significantly strengthens those given in van den Esker (2008) and Jordan (2010). These results, together with our previous work in Li and Peng (2011), build a mathematical foundation for the study of both communities and the small-community phenomenon in various networks. In the proof of the power law degree distribution, we develop the method of alternating concentration analysis to build a concentration inequality by alternately and iteratively applying both the sub- and super-martingale inequalities, which seems to be a powerful technique with further potential applications. © Copyright Cambridge University Press 2012.; We investigate several geometric models of networks that simultaneously have some nice global properties, including the small-diameter property, the small-community phenomenon, which is defined to capture the common experience that (almost) everyone in society also belongs to some meaningful small communities, and the power law degree distribution, for which our result significantly strengthens those given in van den Esker (2008) and Jordan (2010). These results, together with our previous work in Li and Peng (2011), build a mathematical foundation for the study of both communities and the small-community phenomenon in various networks. In the proof of the power law degree distribution, we develop the method of alternating concentration analysis to build a concentration inequality by alternately and iteratively applying both the sub- and super-martingale inequalities, which seems to be a powerful technique with further potential applications. © Copyright Cambridge University Press 2012. |
| Indexed Type | EI ; SCI |
| Keyword | Mathematical Techniques |
| Department | (1) State Key Laboratory of Computer Science Institute of Software Chinese Academy of Sciences P.O. Box 8718 Beijing 100190 China; (2) School of Information Science and Engineering Graduate University of China Academy of Sciences China |
| Subject | Computer Science |
| Sponsorship | NSFC 60325206; Chinese Academy of Sciences; Institute of Software, Chinese Academy of Sciences |
| Language | 英语 |
| WOS ID | WOS:000303819500001 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/14908 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Li Angsheng,Peng Pan. the small-community phenomenon in networks[J]. Mathematical Structures in Computer Science,2012,22(3):373-407. |
| APA | Li Angsheng,&Peng Pan.(2012).the small-community phenomenon in networks.Mathematical Structures in Computer Science,22(3),373-407. |
| MLA | Li Angsheng,et al."the small-community phenomenon in networks".Mathematical Structures in Computer Science 22.3(2012):373-407. |
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