Graff is kind of like an author of Ender’s story – he stands behind the action (mostly), he makes things happen, and he’s kind of a jerk. Also, he secretly loves Ender like a father (which is nice, since Ender’s father is pretty much a no-show in this book), but a father who doesn’t mind putting his son through a lot of pain. “It builds character” is what Graff would probably say.
It may be interesting to compare Graff to Ender’s parents and teachers, except that those parent and teachers play only tiny roles. In that case, let’s just come out and say it: Graff is pretty much the Authority Figure of this book. Although, that doesn’t mean that he’s just that. It’s not like he comes into a room and says, “I’m the authority, I’m here to speak authoritatively, and author author author.” He has a few character traits that make him seem more like a regular character; for instance, as he stresses out over Ender during the novel, he gains a lot of weight.
But no matter how much he eats, Graff is in an interesting position, because when he says something, we might trust him. He doesn’t know everything (see his discussion with Imbu on the mind game at the beginning of Chapter 9 for an example of him not knowing something), but he knows a lot.
That's interesting to us because one of Graff’s favorite topics is how good Ender is. For some random instances of that, just off the top of our heads, check out 4.9 (Ender is a sweet kid), 4.100 (“He’s clean. Right to his heart, he’s good”), 9.295 (where he agrees with Val that Ender is good), and 14.399 (when Graff and Mazer tell Ender that he’s totally innocent).
The big question: Is Graff really correct when he says these things? Or is this one of those areas where he doesn’t know what he’s talking about but knows how to sound like he does?