  This paper treats a blind detection problem to identify the central nodes in
a graph from filtered graph signals. Unlike prior works which impose strong
restrictions on the data model, we only require the underlying graph filter to
satisfy a low pass property with a generic low-rank excitation model. We treat
two cases depending on the low pass graph filter's strength. When the graph
filter is strong low pass, i.e., it has a frequency response that drops sharply
at the high frequencies, we show that the principal component analysis (PCA)
method detects central nodes with high accuracy. For general low pass graph
filter, we show that the graph signals can be described by a structured factor
model featuring the product between a low-rank plus sparse factor and an
unstructured factor. We propose a two-stage decomposition algorithm to learn
the structured factor model via a judicious combination of the non-negative
matrix factorization and robust PCA algorithms. We analyze the identifiability
conditions for the model which lead to accurate central nodes detection.
Numerical experiments on synthetic and real data are provided to support our
findings. We demonstrate significant performance gains over prior works.
