  This paper is concerned with the blind identification of graph filters from
graph signals. Our aim is to determine if the graph filter generating the graph
signals is first-order lowpass without knowing the graph topology. Notice that
lowpass graph filter is a common prerequisite for applying graph signal
processing tools for sampling, denoising, and graph learning. Our method is
inspired by the Perron Frobenius theorem, which observes that for first-order
lowpass graph filter, the top eigenvector of output covariance would be the
only eigenvector with elements of the same sign. Utilizing this observation, we
develop a simple detector that answers if a given data set is produced by a
first-order lowpass graph filter. We analyze the effects of finite-sample,
graph size, observation noise, strength of lowpass filter, on the detector's
performance. Numerical experiments on synthetic and real data support our
findings.
