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We prove local convergence results for the uniformly random, labelled orunlabelled, graphs from subcritical families. As an example special case, weprove Benjamini-Schramm convergence for the uniform random unlabelled tree. Weintroduce a compactification of the space of countable (connected) rootedgraphs, and use it to generalise the notion of Benjamini-Schramm convergence inorder to allow for vertices of infinite degree in the limit object.

Limits of subcritical random graphs and random graphs with excluded minors