In image and signal processing, the conventional wavelet transform is used. In this,the signal is decomposed into a combination of known signals. To analyse the contribution of an individual, the original signal’s behaviour can be inferred. In this article, an overview of the extension of this theory into graph domains ispresented as an introductory by the author’s. In this we are about to review the graph Fourier transform and graph wavelet transforms. These transforms are based on dictionaries of graph spectral filters, namely, spectral graph wavelet transforms. By this we present the main features of the graph wavelet transforms using real and synthetic data. The challenging problem that has been faced is to visualize time-varying data defined on the nodes of a graph. As a result we show our approach using synthetic as well as a real data set.