Wikipedia states that three different graph implementations that are used in practice:

• Adjacency Lists
• Adjacency Matrix
• Incidence Matrix

While I was learning about these structures, another implementation occurred to me that seems to have better asymptotic properties than Wikipedia's. My idea is to create a hash map where the keys are (vertex, vertex) pairs and the values are the cost of their edge.

Given that inserting into and querying from a hash map is $O(1)$, I believe the time complexity would be the following:

• Store graph: $O(E)$
• Add vertex: $O(1)$
• Add edge: $O(1)$
• Remove vertex: $O(V)$
• Remove edge: $O(1)$
• Query cost between vertices: $O(1)$

Since this implementation has strictly better time and space complexity then all three options listed, I'm confused as to why this option isn't.

Why isn't this implementation used in practice?