Data, big or small, in social networks, evolutionary dynamics, the world-wide-web, or citation networks are indexed by social agents, individuals of a population, web sites, or authors all very different from time marks or image pixels. The relations among these data are captured by a graph and not as simple as with data samples in traditional time series, speech or audio signals, nor as with color samples in images, video, or other multidimensional signals. We extend the traditional concepts, tools, and algorithms in discrete signal processing (DSP), including shift, filter, impulse and frequency response, spectrum, Fourier transform and others and use them to analyze and process signals defined in graphs. Applications illustrate our framework.Work with Dr. Aliaksei Sandryhaila and graduate student Stephen Kruzick. José M. F. Moura is Philip and Marsha Dowd University Professor at Carnegie Mellon University, with interests in statistical and algebraic signal processing (SP), currently emphasizing distributed SP on graphs. He was the principal investigator of Spiral (www.spiral.net), an interdisciplinary project for automatic generation of software, hardware, or co-designed hardware/software high quality implementations of SP applications. He is an IEEE Board Director, he was President of the IEEE Signal Processing Society (SPS), and was Editor in Chief for the Transactions on SP. Moura was awarded the 2010 IEEE SPS Technical Achievement Award and the 2012 IEEE SPS Society Award for outstanding technical contributions and leadership in SP. He is a Fellow of IEEE, a Fellow of AAAS, a corresponding member of the Academy of Sciences of Portugal, and a member of the US National Academy of Engineers.