In this paper, we explore the use of graph-basedtransforms to capture correlation in light fields. We consider a scheme in which view synthesis is used as a first step to exploit inter-view correlation. Local graph-based transforms (GT) are then considered for energy compaction of the residue signals. The structure of the local graphs is derived from a coherent super-pixel over-segmentation of the different views. The GT is computed and applied in a separable manner with a first spatial unweighted transform followed by an inter-view GT. For the inter-view GT, both unweighted and weighted GT have been considered. The use of separable instead of non separable transforms allows us to limit the complexity inherent to the computation of the basis functions. A dedicated simple coding scheme is then described for the proposed GT based light field decomposition. Experimental results show a significant improvement with our method compared to the CNN view synthesis method and to the HEVC direct coding of the light field views.