Graph databases are built a lot of different ways; for example Neo4j's architecture is very, very different than something like an RDF triple store, or datastax on top of cassandra.
In graphs you have to persist nodes and edges, though you may partition nodes by label/category. In the case of neo4j there is a property store rather than a set of columns.
[Neo4j internals can be seen here](https://www.slideshare.net/thobe/an-overview-of-neo4j-intern...)...it's a bit old but I think mostly still accurate.
In graphs you have to persist nodes and edges, though you may partition nodes by label/category. In the case of neo4j there is a property store rather than a set of columns.