Light Yagami's relationships with his adversaries in the anime "Death Note" are significant because they serve as a central aspect of the plot development and character growth. These relationships showcase the complexity of Light's character as he engages in a psychological battle of wits with his adversaries, such as L and Near. The dynamic between Light and his adversaries also highlights themes of morality, justice, and the thin line between good and evil. Ultimately, these relationships contribute to the suspense and intensity of the story as Light's actions and decisions are challenged by those who oppose him.