The main objective of work package 2 is to investigate discrete representations of nonlocal methods. We identify finite weighted graphs as suitable mathematical structures to formulate nonlocal approaches on discrete data. We aim to find out which properties of continuum PDE models are approximately preserved after these models are discretized on a graph and which modifications should be made in the assumptions and proofs of these properties to account for the discrete nature of the graph model. Successful understanding of the differences and similarities between continuum and graph models will allow us to translate the large body of work on the properties of PDE models to the discrete framework and will serve to inform which PDE-derived discrete models can be used to address specific graph based questions, such as the detection of structures in graphs (e.g., in community detection). Moreover, we are interested in different graph construction methods and the automatic determination of the optimal neighborhood size for semi-local graph constructions. Related to this issue we will develop different similarity features, such as non-square and transformation-invariant patches. Furthermore, we will investigate the potential of different similarity measures for optimal feature comparison, e.g., Young measures. Finally, we want to work on incremental refinement strategies for finite weighted graphs, which can be applied, e.g., to dynamic data.