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The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.

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Random graphs defined by a set of tiles

You may be interested in research by Nicolas Trotignon, among others, which is somewhat complementary: characterising families of graphs by a subset of patterns (graphs) that do not appear in them. E. …
Christophe Priieur's user avatar