graph data structure is parent of tree, code execution/ function call stacks work like a tree, think flame graphs.
stacks and pointers are baked in assembly and cpu architecture. your claims can't be farther from the truth.
That should provides you some more context about my earlier comment.
By definition of concept (think conceptnet) anything is a concept. Any noun is a concept. Graph theory defines graph as set of two more sets. The set of nodes and set of edges, where each edge itself is set of two nodes (or tuple of two nodes if directionality of the edge also needs to be encoded). A node is anything that you can consider putting into set. And according to set theory, a set is well defined collection of things.
According web ontology language, a "thing" is the root of all things that can exist (see https://www.w3.org/TR/owl-ref/, specifically owl:Thing), except "nothing" maybe.
What all this means is a graph is collection of things, with things pointing to each other sometimes.
Pointers are the underlying data type that makes all other higher level data structures possible, including arrays, matrices, hashmaps, graphs, structs and more.
It can refer to either.
Any concrete data structure that uses indirection — which means pretty much anything more complicated than dense arrays and records — is indeed a form of graph.
But graphs, and more constrained forms like DAGs and trees, can also be abstract data types, implemented by a variety of concrete representations.
One of life’s little ironies is that implementing a general abstract graph using a general concrete graph whose records and pointers correspond (roughly) 1:1 with the nodes and edges in the abstract graph is often a poor choice.
Moreover, it’s not unusual to have an abstract graph implemented using a non-graph data structure (for example, a dense adjacency matrix) or to use a graph-like data structure to implement an abstract data type whose interface doesn’t look particularly graph-like (for example, a piece table).
A graph is a group of two sets, the set of nodes and set of edges.
As an abstract data type, you may define operations on the data structure (aka abstract data type).
In case of graph, for example, you can define connectivity check (existence of an edge). And graph theory provides plenty more.
And set (in set theoretic sense) is also a data structure, you may define the membership check as on operation on that.
On the other hand, a data type is a tag that a compiler associates with raw bits and bytes on the memory in order to operate on them. Examples, datetime is a data type, string is a data type, array is a data type, numbers are data type, these are not data structures. These are language primitives.
Further graph is superseded by hi-graph (which is foundation for relational data bases and tuple algebra), and subseded by for example DAGs and trees.
To build an edge in a graph, you need something that could point to something. Like A points to B, the most fundamental way to capture this mapping is by using pointers (that is the address of B, stored at a known location accessible by A). A->B or A.B are just syntactic elements that underlie this.
Arrays, Matrices, Structs, Strings, are all made possible by pointers.
Pointers are a data type, it tags the value (usually in range 0..usize), as being an address of something else in the memory. Pointers are not data structures.
I should say primitives vs non-primitives if that makes the difference between what is data type vs data structure.