One of the more complex and important relationships in the game is Sabin and Edgar's. Sabin respects Edgar, but more than that Sabin looks up to him and trusts Edgar with his life. Edgar takes care of Sabin, and it's kind of sweet in a brotherly way. They're twin brothers, they're best friends, and they're the only family each other has.
I think that once their parents died, Edgar felt like he needed to take care of Sabin. They're twin brothers, but Edgar was born a little before Sabin making him Sabin's big brother, and Sabin calls him "Big Brother" all the time. I think that some of Edgar's decisions made for Sabin extend past a normal brother to brother relationship, though. Some of the things Edgar does like sacrificing his own happiness and freedom so that Sabin could be free are things that a parent would do. Sabin was a lot more immature than Edgar when their father died, and seemed to take it a lot harder, so I think that Edgar felt like Sabin needed him. Perhaps that's why Edgar didn't cry on the night their father died. He probably felt like he had to be strong for Sabin.
Edgar obviously loved Sabin, and I think that he loved Sabin more than he loved himself. He spoke of Sabin in high regard, and he did anything he could to give Sabin everything he wanted. Even when Sabin wanted to leave Figaro, Edgar didn't stop him. He let him go, and didn't see him again for ten years.
When they reconnect, it's almost like they were never apart. Edgar and Sabin pick on each other, they reminisce together, and they toast their parents together. Edgar seemed happy to have his little brother around him again, and he was actually proud to have Sabin as his brother, even though Terra saw Sabin as a bodybuilder who strayed from his gym.
Sabin thought highly of Edgar as well, evident from what he told Terra when she was thinking about joining the Returners.
The only thing I can add is that you can trust my brother implicitly. He's always been fair with me. You can trust him, Terra... But don't you DARE tell him I said that!
He doesn't just think highly of Edgar, though; he looks up to him. I would argue that Edgar is the inspiration if not motivation behind most of Sabin's actions in the game. Edgar could do no wrong in Sabin's eyes, and Edgar is who Sabin aspired to be more like.
Most importantly, Sabin loved his brother. Sabin doesn't find out what his brother did for him on the night of the coin toss until later in the game, but I think he always knew his brother loved him, too. He just didn't know how much. He discovers that love before the game is over, though, and it's pretty cool when he comes to that realization.
I have come to experience anew the love of my brother!
I think that even though Sabin was able to spend ten years apart from Edgar, he realized that he needed Edgar. He needed family. With Edgar is where he truly belonged.