Vertex-varying spectral content on graphs challenges the assumption of vertex invariance and requires vertex-frequency representations to adequately analyze them. The localization window in graph Fourier transform plays a crucial role in this analysis. An analysis of the window functions is presented. The corresponding spectrograms are considered from the energy condition point of view as well. Like in time-frequency analysis, the distribution of signal energy as a function of the vertex and spectral indices is an alternative way to approach vertex-frequency analysis. After an introduction to the second part of this chapter, a local smoothness definition, a definition of an ideal form of the vertex-frequency energy distributions, and two energy forms of the vertex-frequency representations are given. A graph form of the Rihaczek distribution is used as the basic distribution to define a class of reduced interference vertex-frequency energy distributions. These distributions reduce cross-terms effects and satisfy graph signal marginal properties. The theory is illustrated through examples.