Final Report Summary - SUBLINEAR (Sublinear algorithms for the analysis of very large graphs) Goal of this project has been to improve our understanding of sampling algorithms that obtain information about the structure of very large graphs. We approached this problem from a complexity theory point of view in the framework of property testing: We wanted to understand which classes of problems can be solved approximately using random sampling. Our results include new sampling algorithms for directed graphs when the edges can be seen only from the origin (like in the webgraph) that were achieved by deriving a relation to sampling algorithms that can access the edges from both sides. We also developed sampling algorithms for testing whether a graph has a cluster structure, for approximating the spectrum of a graph, and for testing whether a graph is a k-nearest neighbor graph. We made progress on the development of sampling algorithms with one-sided error, i.e. algorithms that reject only if they find a counter-example to the tested "hypothesis". Furthermore, we improved our understanding of sampling algorithms in specific graph classes such as planar graphs.