What is Ender's relationship with various characters in the book?
One way to look at Ender's relationships in the book is from the perspective of need. Does Ender need this character, or does this character need Ender? Do they need each other?
Ender and Peter are brothers, but enemies. Peter hates Ender and Ender fears Peter, almost throughout the entire book. However, Peter serves as a motivation for Ender to succeed, so Ender does need him.
Ender and Valentine are brother and sister and this is one relationship that Ender mostly trusts. Valentine loves Ender unconditionally, and Ender loves her back. Ender needs Valentine's love to remind him that he is human.
Graff is in charge of Ender's education. Graff needs Ender, and uses him. Ender does not have a personal connection to Graff, except to be his pupil and to expect anything and everything from him. He knows Graff is manipulating him to train him.
Ender is Bean's commander and teacher. At first, it seems that Bean needs Ender, because Ender is the best student commander. However, it quickly becomes apparent that Bean might be the only student in Battle School who is as smart, or smarter, than Ender. Therefore, Ender comes to rely on Bean for ideas, creativity, and as an intellectual outlet that he cannot find from other students.