Is this a counter example to the Eulerian Trail definition?

Question

Wikipedia says:

An undirected graph has an Eulerian trail if and only if exactly zero or two vertices have odd degree, and all of its vertices with nonzero degree belong to a single connected component.

However, I was able to produce this graph which appears to

1. Break the definition (all 8 vertices have an odd degree of 3)
2. Allow for a Eulerian path: $A\to C\to E\to G\to D\to F\to H\to B$

Is there something I missed/misunderstood here?

Answer 1

Whoops, I misread. The definition of a Eulerian trail is a path that visits every edge exactly once, not every vertex.

The concept I was thinking of is called a Hamiltonian path which visits each vertex exactly once.