In this work, we study the properties of sampling sets on families of large
graphs by leveraging the theory of graphons and graph limits. To this end, we
extend to graphon signals the notion of removable and uniqueness sets, which
was developed originally for the analysis of signals on graphs. We state the
formal definition of a $\Lambda-$removable set and conditions under which a
bandlimited graphon signal can be represented in a unique way when its samples
are obtained from the complement of a given $\Lambda-$removable set in the
graphon. By leveraging such results we show that graphon representations of
graphs and graph signals can be used as a common framework to compare sampling
sets between graphs with different numbers of nodes and edges, and different
node labelings. Additionally, given a sequence of graphs that converges to a
graphon, we show that the sequences of sampling sets whose graphon
representation is identical in $[0,1]$ are convergent as well. We exploit the
convergence results to provide an algorithm that obtains approximately close to
optimal sampling sets. Performing a set of numerical experiments, we evaluate
the quality of these sampling sets. Our results open the door for the efficient
computation of optimal sampling sets in graphs of large size.

我们研究了利用图测度和图极限理论来研究大型图的采样集的特性。我们将可移除集合和唯一性集合的概念扩展到图测度上，并给出了一些条件，当从图测度的可移除集合的补集中获取样本时，带宽限制的图测度信号可以以唯一的方式表示。我们利用这些结果，将图测度上的图和图信号的表示形式用作比较具有不同节点数量、边数量和节点标记的图之间的采样集的共同框架。此外，对于收敛于图测度的图的序列，我们还展示了具有相同图测度表示形式的采样集的序列也是收敛的。我们利用这种收敛结果提出了一种获得近乎最优采样集的算法，并通过一组数字实验评估了这些采样集的质量。我们的结果为大型图中高效计算最优采样集提供了可能。