Hermione Granger is not a half-blood. She is a pure-blood witch.
This is confirmed in the books, where her parents, Mr. and Mrs. Granger, are both wizards.
While Hermione's parents are not particularly magical, they are both full-blooded wizards, making Hermione a pure-blood witch.
The term "half-blood" refers to wizards and witches born to one magical parent and one non-magical parent.
For example, Harry Potter is a half-blood, as his father, James Potter, was a wizard, and his mother, Lily Evans, was a witch.
Hermione's pure-blood status is never questioned in the books, and it is never suggested that she has any non-magical ancestry.
Therefore, Hermione Granger is a pure-blood witch, not a half-blood.
