Graduate Thesis Or Dissertation
Characterizing the tails of degree distributions in real-world networks 公开 Deposited
- Abstract
This is a thesis about how to characterize the statistical structure of the tails of degree distributions of real-world networks. The primary contribution is a statistical test of the prevalence of scale-free structure in real-world networks. A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree k follows a power law, decaying like k⁻α, often with 2 < α< 3. However, empirical evidence for this belief derives from a relatively small number of real-world networks. In the first section, we test the universality of scale-free structure by applying state-of-the-art statistical tools to a large corpus of nearly 1000 network data sets drawn from social, biological, technological, and informational sources. We fit the power-law model to each degree distribution, test its statistical plausibility, and compare it via a likelihood ratio test to alternative, non-scale-free models, e.g., the log-normal. Across domains, we find that scale-free networks are rare, with only 4% exhibiting the strongest-possible evidence of scale-free structure and 52% exhibiting the weakest-possible evidence. Furthermore, evidence of scale-free structure is not uniformly distributed across sources: social networks are at best weakly scale free, while a handful of technological and biological networks can be called strongly scale free. These results undermine the universality of scale-free networks and reveal that real-world networks exhibit a rich structural diversity that will likely require new ideas and mechanisms to explain. A core methodological component of addressing the ubiquity of scale-free structure in real-world networks is an ability to fit a power law to the degree distribution. In the second section, we numerically evaluate and compare, using both synthetic data with known structure and real-world data with unknown structure, two statistically principled methods for estimating the tail parameters for power-law distributions, showing that in practice, a method based on extreme value theory and a sophisticated bootstrap and the more commonly used method based an empirical minimization approach exhibit similar accuracy.
- Creator
- Date Issued
- 2019
- Academic Affiliation
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- Committee Member
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- Commencement Year
- Subject
- 最新修改
- 2020-01-13
- Resource Type
- 权利声明
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缩略图 | 标题 | 上传日期 | 公开度 | 行动 |
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characterizingTheTailsOfDegreeDistributionsInRealWorldNe.pdf | 2019-11-15 | 公开 | 下载 |