从图子中抽取的大型图的Laplacian谱
The Laplacian Spectrum of Large Graphs Sampled from Graphons
摘要：
研究了从图子中抽取的（大）图的Laplacian谱和平均有效电阻。广义地说，我们的主要发现是，一个大的稠密图的拉普拉斯特征值可以有效地近似使用相应的图子的度函数。更具体地说，我们展示了如何近似的拉普拉斯特征值的分布和平均有效电阻（基尔霍夫指数）的图形。对于所有的情况下，我们提供了明确的边界上的近似误差，并推导出渐近速率时，误差为零时，节点的数量趋于无穷大。我们的主要结果是在图子是分段Lipschitz且远离零有界的条件下得到的。
英文摘要：
This paper studies the Laplacian spectrum and the average effective resistance of (large) graphs that are sampled from graphons. Broadly speaking, our main finding is that the Laplacian eigenvalues of a large dense graph can be effectively approximated by using the degree function of the corresponding graphon. More specifically, we show how to approximate the distribution of the Laplacian eigenvalues and the average effective resistance (Kirchhoff index) of the graph. For all cases, we provide explicit bounds on the approximation errors and derive the asymptotic rates at which the errors go to zero when the number of nodes goes to infinity. Our main results are proved under the conditions that the graphon is piecewise Lipschitz and bounded away from zero.
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