I meant that the Neo4j API offers methods for graph traversal out-of-the-box which are likely the same ones that most people will use. MySQL doesn't have a default data structure for graphs (that I know of) or default algorithms.

So while the methods used to traverse the Neo4j graph are fairly representative, the data structure and algorithms used for the MySQL traversal are not.

Of course, I agree with you that the data structure itself is optimized. In general I'm not doubting Neo4j's ability to excel in most benchmarks. I just think the approach is very basic.