A tree is a graph. A typical Java-style object composing other objects composing other objects again, etc etc, often with cycles and parent backreferences and whatnot, is a graph. The html DOM is a graph.
I recognize that these are often very tree-like, which feels like cheating in the same way as saying “well a list is also a graph!” is. But given that cycles are common enough that serializers (eg JSON.stringify) need to special-case those, I think maybe this is simply not true, and they’re really just graphs. Very few tree-like class structures tend to remain pure trees.
The only thing missing from references/pointers to be able to represent what the author is looking for, is having data on the edges. I think this is trivially solvable by putting nodes halfway the edge (= add a level of indirection, an operation so common that we don’t even think of it as “adding data to the edges”).
So I think the answer is that there’s no explicit data structure named “graph” because the basic building block of composition in nearly every language (reference/pointer) is an edge, and the basic building block of data representation (objects/structs/records) is a node. So for most graphs, trying to pour it all into some fancy Graph<V, E> datastructure feels like needless complexity.