@S.Yu - LION is a bit more complex than that. It all depends how the battery is made. For example, more silicon in annode makes the battery more energy dense but sacrifices lifespan.
The best way to explain it is like cooking, even with same ingredients, how you structure it and the mix ratio and usage can make a world of difference. So sometimes one can sacrifice improvement in energy density to increase the lifespan so that they can increase the speed it recharges.
Trying to look up Huwaii's case, there were 2 mentions of graphene, one for the energy storage industry where they improved thermal management. And another about a rumored phone where the battery is less energy dense but charges much quicker. There is not much info on the 2nd one since its merely a rumor.
So I found no reference so far of Huwaii doing the same thing, do you have a link?