In this talk, we present a novel generalization of 
the graph Fourier transform (GFT). Our approach is based on 
separately considering the definitions
of signal energy and signal variation, leading to several possible
orthonormal GFTs. Our approach includes traditional definitions of
the GFT as special cases, while also leading to new GFT designs that
are better at taking into account the irregular nature of the graph. 
As an illustration, in the context of 
sensor networks we use the Voronoi cell area of vertices in our GFT
definition, showing that it leads to a more sensible definition of
graph signal energy even when sampling is highly irregular.