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So I was reading this and it got me thinking, because i've noticed traits of both alpha and beta in both Naruto and Sasuke. In both of them, they do what they want when they want, and never get hung up on who their actions affect. According to that article, their spontaneous decision making is an alpha trait.
However what isn't alpha is Naruto desiring the acceptance of others, because a real alpha could give less of a damn what other people think. In Sasuke, he doesn't have this issue, but what he does have is a tendency to blame others for things they didn't do like how he blamed the leaf village for the Uchiha Massacre even though they were mostly ignorant to the reality of the situation or his tendency to sulk and play victim and letting his self-pity cloud his judgement. Also, while Naruto has little qualms proclaiming his sexuality or exposing it in others Sasuke shows little interest in woman, which is alpha in some ways, but beta in the fact he shows absolutely zero interest in woman outside the bedroom.