According to the article, the physical implementation of graphs is precisely the thing you cannot ignore, because the performance difference between a generic s

According to the article, the physical implementation of graphs is precisely the thing you cannot ignore, because the performance difference between a generic solution and a "correct" solution is huge, basically the difference between the algorithm not completing and the algorithm completing. That's the reason why it's hard to come up with a single one-size-fits-all graph implementation.