  We study signal recovery on graphs based on two sampling strategies: random
sampling and experimentally designed sampling. We propose a new class of smooth
graph signals, called approximately bandlimited, which generalizes the
bandlimited class and is similar to the globally smooth class. We then propose
two recovery strategies based on random sampling and experimentally designed
sampling. The proposed recovery strategy based on experimentally designed
sampling is similar to the leverage scores used in the matrix approximation. We
show that while both strategies are unbiased estimators for the low-frequency
components, the convergence rate of experimentally designed sampling is much
faster than that of random sampling when a graph is irregular. We validate the
proposed recovery strategies on three specific graphs: a ring graph, an
Erd\H{o}s-R\'enyi graph, and a star graph. The simulation results support the
theoretical analysis.
