标题： 无标度网络是罕见的 显示英文标题

标题： Scale-free networks are rare

摘要： 现代网络科学的一个核心观点是，现实世界中的网络通常是“无标度的”，这意味着度数为$k$的节点的比例遵循幂律，衰减类似于$k^{-\alpha}$，通常具有$2 < \alpha < 3$。 然而，这种信念的实证证据来自于相对较少的现实世界网络。 我们通过将最先进的统计工具应用于从社会、生物、技术和信息源中抽取的近1000个网络数据集的大型语料库，来测试无标度结构的普遍性。 我们将幂律模型拟合到每个度分布，检验其统计合理性，并通过似然比检验将其与替代的非无标度模型进行比较，例如对数正态分布。 在各个领域中，我们发现无标度网络很少见，只有4%表现出最强可能的无标度结构证据，52%表现出最弱可能的证据。 此外，无标度结构的证据在不同来源中并不均匀分布：社交网络最多只能弱无标度，而少数技术和生物网络可以被称为强无标度。 这些结果削弱了无标度网络的普遍性，并揭示了现实世界网络表现出丰富的结构多样性，这很可能需要新的想法和机制来解释。 显示英文摘要

摘要： 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 $k^{-\alpha}$, often with $2 < \alpha < 3$. However, empirical evidence for this belief derives from a relatively small number of real-world networks. 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.