Original:  However, the exact nature of the relation is not clear since Socrates was known for his self-restraint, while Alcibiades admits in the Symposium that he had tried to seduce Socrates but failed.
Revised:  However, the exact nature of his relationship with Alcibiades is not clear since Socrates was known for his self-restraint, while Alcibiades admits in the Symposium that he had tried to seduce Socrates but failed.
Edit intent: clarity