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Recently, Goldreich introduced the notion of property testing ofbounded-degree graphs with an unknown distribution. We propose a slightmodification of his idea: the Radon-Nikodym Oracles. Using these oracles anyreasonable graph property can be tested in constant-time against any reasonableunknown distribution in the category of planar graphs. We also discussRandomized Local Distributed Algorithms, which work on very large graphs withunknown distributions. Finally, we discuss how can we learn graph propertiesusing observations instead of samplings.

Learning Very Large Graphs with Unknown Vertex Distributions