Board Thread:Naruto Discussions/@comment-28861328-20140618060932/@comment-20077569-20140619051324

Much like how the Rinnegan got diluded (weakened) into producing the weakened Sharingan of Indra, probabaly the original Byakugan (Hamura's) got weakened to produce the Hyuga clan's byakugan.

Since Neji was reported to have the strongest Byakugan of his generation in the clan, it is likely he had a small amount of Hamura's chakra in him.