  We study the blind centrality ranking problem, where our goal is to infer the
eigenvector centrality ranking of nodes solely from nodal observations, i.e.,
without information about the topology of the network. We formalize these nodal
observations as graph signals and model them as the outputs of a network
process on the underlying (unobserved) network. A simple spectral algorithm is
proposed to estimate the leading eigenvector of the associated adjacency
matrix, thus serving as a proxy for the centrality ranking. A finite rate
performance analysis of the algorithm is provided, where we find a lower bound
on the number of graph signals needed to correctly rank (with high probability)
two nodes of interest. We then specialize our general analysis for the
particular case of dense \ER graphs, where existing graph-theoretical results
can be leveraged. Finally, we illustrate the proposed algorithm via numerical
experiments in synthetic and real-world networks, making special emphasis on
how the network features influence the performance.
