R E L A T I O N S H I P SDON'T READ any of the spoilers below if you don't want it to be spoiled, specially those who have NOT read the manga or watched the anime, this is only for those people who don't really understand their relationships.....
Yuki has love for both Kaname and Zero, and they both love her. Kaname and Zero have a fundamental antagonism towards each other because they are inherently enemies. Kaname occasionally expresses a little jealousy over Yuki's attachment to Zero.
Yuki has loved Kaname since she was a child, they pledged to marry each other to be like their parents and currently she is his fiance. As a human, she falls in love with him and Zero constantly reminds her that she cannot be with Kaname. Kaname in turns advises Zero that he is only allowed to live after biting Yuki, so that he can repay her by protecting her.
After discovering she was a vampire, Zero declares Yuki his enemy and threatens to kill her and all vampires. When Kaname arrives on the scene, Zero shifts his attention to it, they attack one another until Yuki runs in between them. Kaname admits the desire to kill Zero but cannot stand the idea of Yuki hating him. He later walks away telling Yuki that she knows where she belongs.
Yuki tells Zero that her mind is consumed with the desire to drink Kaname's blood, Zero disgustedly admits his beastly desire to drink Yuki's blood and devour her life. While parting, Zero tells Yuki that she should be with the man who will live as long as her. Yuki rejoins Kaname at the Kuran mansion and he tells her that he understands that half her heart belongs to Zero and that he is happy with that since she is at his side. Yuki doesn't believe that Kaname can be happy with simply that.
During the 1 year time skip, Yuki is kept inside the house while she deals with her inability to bite and desperate hunger. Yuki finally admits to Zero also being in her heart, thus her hunger/thirst cannot be quench by Kaname alone. Yuki then asked if its alright for her to stay by Kaname's side. Kaname readily agrees since Yuki wants to be with him always. He impresses upon her that he cannot be without her and would rather die. Yuki later apologises for what she said and that she can clearly see her path.
Prior to the ball, Kaname expresses a little jealousy over Yuki's trust in Zero to do his duty, but is fine with Yuki meeting up with Zero. Following the incident at the hunter's safe house, he tells Yuki that she was good in that she refrained from biting Zero.
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