利用网络局部信息的边缘采样

摘要：

边缘采样是网络分析中的一个重要课题。它提供了一种自然的方式来减少网络规模，同时保留原始网络的所需功能。仅使用本地信息的采样方法在实践中很常见，因为它们不需要访问整个网络，并且可以很容易地并行化。尽管有希望的经验表现，这些方法大多来自启发式的考虑，因此仍然缺乏理论依据。为了解决这个问题，我们在本文中研究了一个简单的边缘采样方案，使用网络的本地信息。我们证明了当局部连通性足够强时，采样网络满足强谱性质。我们通过一个全局参数来量化局部连通性的强度，并将其与更常见的网络统计数据（如聚类系数和网络曲率）联系起来。在此基础上，我们还给出了随机网络和超图可以有效抽样的充分条件。

英文摘要：

Edge sampling is an important topic in network analysis. It provides a natural way to reduce network size while retaining desired features of the original network. Sampling methods that only use local information are common in practice as they do not require access to the entire network and can be parallelized easily. Despite promising empirical performances, most of these methods are derived from heuristic considerations and therefore still lack theoretical justification. To address this issue, we study in this paper a simple edge sampling scheme that uses network local information. We show that when local connectivity is sufficiently strong, the sampled network satisfies a strong spectral property. We quantify the strength of local connectivity by a global parameter and relate it to more common network statistics such as the clustering coefficient and network curvature. Based on this result, we also provide sufficient conditions under which random networks and hypergraphs can be sampled efficiently.

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。