As I see the sentence, there should be a "from" between "graduating" and "high school". How do you see it? Is it good English?
Look at thefreedictionary.com, which quotes definitions from several dictionaries. Recall that a "transitive verb" takes on object, e.g. "graduate high school", while an "intransitive verb" does not, so you would need a prepositional phrase like "graduate from high school".
American Heritage lists "graduate" as being both transitive and intransitive, though it lists the transitive form as a "usage problem".
Collins allows a transitive usage only when the subject is the institution: "The high school graduated Sally despite her failing half her classes", but makes no mention of a transitive form when the subject is the student.
Random House gives exactly the usage you are describing as definition #9: "to receive a degree or diploma from" with the example, "to graduate college".
I routinely hear people say both "graduate from high school" and "graduate high school". Speaking as an American -- I can't address usage in other English-speaking countries.
In British English, we graduate only 'from' somewhere. I graduated from Durham (University) in 1967. We cannot omit 'from'.
We don't normally graduate from a school. If we do not specify the institution, we assume that reference is made to graduating with a bachelor's degree awarded by a university. George graduated in 1084 and then went to America.
Searching the online dictionaries proves you’re right. I couldn’t find any dictionary reference that contradicts you; all indicate the use of “from”.
However, a quick search on google books yields many results without the use of “from”.
Since there are so many writers that use the construction without “from”, we can form the conclusion that both forms are acceptable.
But let English natives put some more light on the issue, and see which one of them is more used.