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The several algebraic approaches to graph transformation proposed in theliterature all ensure that if an item is preserved by a rule, so are itsconnections with the context graph where it is embedded. But there areapplications in which it is desirable, for example when cloning an item, tospecify different embeddings for the original and for the copy. Therefore wepropose a conservative extension of these approaches where a rule can specifyhow the embedding of a preserved item should be changed, typically by removingcertain connections.

AGREE -- Algebraic Graph Rewriting with Controlled Embedding (Long Version)