Compression in the space of graphs

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I'm looking for formal representations, mostly drawing from algebraic graph theory (open to any other framework this could be possible, of course) that are conducive to compression of graphs (networks), something that is not just converting a graph G=(V,E) to it's computer file representation and then compressing the file, but a compression model with a formal generative mathematical description for the compression as well as re-prodution of the original graph from the compressed form. I am not seeing much discussion on graph compression, any thoughts or references would be greatly appreciated.