Graph-based transforms are powerful tools for signal representation and energy compaction. However, their use for high dimensional signals such as light fields poses obvious problems of complexity. To overcome this difficulty, one can consider local graph transforms defined on supports of limited dimension, which may however not allow us to fully exploit long-term signal correlation. In this paper, we present methods to optimize local graph supports in a rate distortion sense for efficient light field compression. A large graph support can be well adapted for compression efficiency, however at the expense of high complexity. In this case, we use graph reduction techniques to make the graph transform feasible. We also consider spectral clustering to reduce the dimension of the graph supports while controlling both rate and complexity. We derive the distortion and rate models which are then used to guide the graph optimization. We describe a complete light field coding scheme based on the proposed graph optimization tools. Experimental results show rate-distortion performance gains compared to the use of fixed graph support. The method also provides competitive results when compared against HEVC-based and the JPEG Pleno light field coding schemes. We also assess the method against a homography-based low rank approximation and a Fourier disparity layer based coding method.