门限网络模型中的普适幂律：基于极值理论的理论分析
Universal power laws in the threshold network model: A theoretical analysis based on extreme value theory
摘要：
我们从理论和数值上研究了具有一般权函数的阈值网络模型，其中有大量的节点和高阈值。我们的分析是基于极值理论，这给了我们一个理论上的理解，在一个足够高的范围内的独立和同分布的随机变量的分布。具体地说，分布一般可以表示为广义帕累托分布，这使我们能够制定通用的重量分布函数。利用该定理，我们得到了度分布和聚类系数的精确表达式，在一定的度范围内，它们表现为普适的幂律。我们还将理论预测与数值结果进行了比较，发现它们非常一致。
英文摘要：
We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a theoretical understanding of the distribution of independent and identically distributed random variables within a sufficiently high range. Specifically, the distribution could be generally expressed by a generalized Pareto distribution, which enabled us to formulate the generic weight distribution function. By using the theorem, we obtained the exact expressions of degree distribution and clustering coefficient which behaved as universal power laws within certain ranges of degrees. We also compared the theoretical predictions with numerical results and found that they were extremely consistent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
