  We consider the problem of sampling from data defined on the nodes of a
weighted graph, where the edge weights capture the data correlation structure.
As shown recently, using spectral graph theory one can define a cut-off
frequency for the bandlimited graph signals that can be reconstructed from a
given set of samples (i.e., graph nodes). In this work, we show how this
cut-off frequency can be computed exactly. Using this characterization, we
provide efficient algorithms for finding the subset of nodes of a given size
with the largest cut-off frequency and for finding the smallest subset of nodes
with a given cut-off frequency. In addition, we study the performance of random
uniform sampling when compared to the centralized optimal sampling provided by
the proposed algorithms.
