  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.
