有向网络的抽样性质
Sampling properties of directed networks
摘要：
对于许多现实世界的网络，只有一个小的“抽样”版本的原始网络可能会被调查，这些结果然后被用来得出有关实际系统的结论。基于流行病过程的广度优先搜索（BFS）抽样的变体被广泛使用。虽然它是公认的BFS采样失败，在大多数情况下，捕捉有向网络的IN组件（S），BFS采样对其他拓扑性质的影响的描述是所有，但缺乏文献。为了系统地研究抽样偏差对有向网络的影响，我们在完全大规模有向网络上比较了BFS抽样和随机抽样。我们提出了新的结果和七个不同的完整的有向网络（采样前），包括三个版本的维基百科，三个不同来源的采样万维网数据的拓扑特性的彻底分析，和基于互联网的社交网络。我们详细的差异，抽样方法和覆盖率可以使这七个网络的抽样版本的结构特性。最值得注意的是，我们发现，抽样方法和覆盖影响蝴蝶结结构，以及在抽样网络中的强连接组件的数量和结构。此外，在低采样覆盖率（小于40%）下，BFS采样网络的平均度、出度方差、度自相关和链路互反性被高估了30%或更多，而当采样覆盖率超过65%时，其值仅在完全网络中相应值的10%以内.这些结果可能会让我们重新思考我们对现实世界有向网络的结构、功能和演化的了解。
英文摘要：
For many real-world networks only a small "sampled" version of the original network may be investigated; those results are then used to draw conclusions about the actual system. Variants of breadth-first search (BFS) sampling, which are based on epidemic processes, are widely used. Although it is well established that BFS sampling fails, in most cases, to capture the IN-component(s) of directed networks, a description of the effects of BFS sampling on other topological properties are all but absent from the literature. To systematically study the effects of sampling biases on directed networks, we compare BFS sampling to random sampling on complete large-scale directed networks. We present new results and a thorough analysis of the topological properties of seven different complete directed networks (prior to sampling), including three versions of Wikipedia, three different sources of sampled World Wide Web data, and an Internet-based social network. We detail the differences that sampling method and coverage can make to the structural properties of sampled versions of these seven networks. Most notably, we find that sampling method and coverage affect both the bow-tie structure, as well as the number and structure of strongly connected components in sampled networks. In addition, at low sampling coverage (i.e. less than 40%), the values of average degree, variance of out-degree, degree auto-correlation, and link reciprocity are overestimated by 30% or more in BFS-sampled networks, and only attain values within 10% of the corresponding values in the complete networks when sampling coverage is in excess of 65%. These results may cause us to rethink what we know about the structure, function, and evolution of real-world directed networks.
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