Comment by WorldMaker

Even the raw storage for graphs doesn't have just one answer: you could store edge lists or you could store adjacency matrixes. Some algorithms work better with one, some work better with the other. You probably don't want to store both because that can be extra memory overhead as well as a locking problem if you need to atomically update both at once. You probably don't want to automatically flip back and forth between representations because that could cause garbage collector churn if not also long breadth or depth searches, and you may not want to encourage manual conversions between data structures either (to avoid providing a performance footgun to your users). So you probably want the edge list Graph type and the adjacency matrix Graph type to look very different, even though (they are trivially convertible they may be expensive to convert as mentioned), and yeah that's the under-the-hood storage mechanism. From there you get into possible exponential explosion as you start to get into the other higher level distinctions between types of graphs (DAGs versus Trees versus cyclic structures and so forth, and all the variations on what a node can be, if edges can be weighted or labeled, etc).