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.

对近 1000 个来自社交、生物、技术和信息等领域的网络数据集，应用最先进的统计工具来测试无尺度结构及其普遍适用性。结果发现，真实世界中的网络具有丰富的结构多样性，其无尺度结构是罕见的，并不具有普适性。而社交网络的结构是弱无尺度的，而少数技术和生物网络则具有强无尺度结构。

无尺度网络罕见

Scale-free networks are rare

High energy cosmic ray electrons plus positrons (CREs), which lose energy
quickly during their propagation, provide an ideal probe of Galactic
high-energy processes and may enable the observation of phenomena such as
dark-matter particle annihilation or decay. The CRE spectrum has been directly
measured up to $\sim 2$ TeV in previous balloon- or space-borne experiments,
and indirectly up to $\sim 5$ TeV by ground-based Cherenkov $\gamma$-ray
telescope arrays. Evidence for a spectral break in the TeV energy range has
been provided by indirect measurements of H.E.S.S., although the results were
qualified by sizeable systematic uncertainties. Here we report a direct
measurement of CREs in the energy range $25~{\rm GeV}-4.6~{\rm TeV}$ by the
DArk Matter Particle Explorer (DAMPE) with unprecedentedly high energy
resolution and low background. The majority of the spectrum can be properly
fitted by a smoothly broken power-law model rather than a single power-law
model. The direct detection of a spectral break at $E \sim0.9$ TeV confirms the
evidence found by H.E.S.S., clarifies the behavior of the CRE spectrum at
energies above 1 TeV and sheds light on the physical origin of the sub-TeV
CREs.

使用 DArk Matter Particle Explorer（DAMPE）对 25 GeV 至 4.6 TeV 的 CRE 进行高能分辨率和低背景的直接检测，发现一个能级为 0.9 TeV 的谱隙，证实了 H.E.S.S. 的发现，阐明了 1 TeV 以上能量的 CRE 的物理起源。