This paper introduces a framework for discrete signal processing (DSP) on graphs, extending traditional DSP concepts to signals indexed by nodes of a graph. The framework includes filters, convolution, z-transform, impulse response, spectral representation, and Fourier transform, and is applied to classify blogs, linear predict and compress data from irregularly located weather stations, and predict customer behavior of a mobile service provider. The paper discusses the structure of signals on graphs, graph filters, and the graph Fourier transform, emphasizing the difference between the graph Fourier transform based on the graph Laplacian and the proposed approach based on the adjacency matrix. It also presents applications of the framework in signal compression, linear prediction, and data classification. The paper highlights the importance of graph representation in signal processing and demonstrates the effectiveness of the framework in various DSP tasks.This paper introduces a framework for discrete signal processing (DSP) on graphs, extending traditional DSP concepts to signals indexed by nodes of a graph. The framework includes filters, convolution, z-transform, impulse response, spectral representation, and Fourier transform, and is applied to classify blogs, linear predict and compress data from irregularly located weather stations, and predict customer behavior of a mobile service provider. The paper discusses the structure of signals on graphs, graph filters, and the graph Fourier transform, emphasizing the difference between the graph Fourier transform based on the graph Laplacian and the proposed approach based on the adjacency matrix. It also presents applications of the framework in signal compression, linear prediction, and data classification. The paper highlights the importance of graph representation in signal processing and demonstrates the effectiveness of the framework in various DSP tasks.