We consider the problem of estimating a network's eigenvector centrality only from data on the nodes, with no information about network topology. Leveraging the versatility of graph filters to model network processes, data supported on the nodes is modeled as a graph signal obtained via the output of a graph filter applied to white noise. We seek to simplify the downstream task of centrality ranking by bypassing network topology inference methods and, instead, inferring the centrality structure of the graph directly from the graph signals. To this end, we propose two simple algorithms for ranking a set of nodes connected by an unobserved set of edges. We derive asymptotic and non-asymptotic guarantees for these algorithms, revealing key features that determine the complexity of the task at hand. Finally, we illustrate the behavior of the proposed algorithms on synthetic and real-world datasets.

中文翻译：

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特征向量中心性排序的盲推

我们考虑仅从节点上的数据估计网络的特征向量中心性的问题，而没有关于网络拓扑的信息。利用图滤波器的多功能性来模拟网络过程，节点上支持的数据被建模为通过应用于白噪声的图滤波器的输出获得的图信号。我们试图通过绕过网络拓扑推理方法来简化中心性排序的下游任务，而是直接从图信号推断图的中心性结构。为此，我们提出了两种简单的算法来对由一组未观察到的边连接的一组节点进行排序。我们为这些算法推导出渐近和非渐近保证，揭示决定手头任务复杂性的关键特征。最后，