Wow, what a tough question. No 'all of the above'? LOL
Well, it was easy to strike a few of them out. While Ron is an integral part of the trio, he really doesn't contribute to the Harry/Hermione relationship, just like Harry doesn't contribute much to Ron's with Hermione; thus, not him. Definitely not similarities, because Harry is as different from Hermione as Ron is from her. Friendship is no go either; what makes H/Hr close is because they possess something extra that makes them close.
That leaves trust, faith, understanding, and the limited 'telepathy' between the two. I really group understanding with communicatiing without words, because unless H/Hr truly have telepathic powers, the reason they can communicate without words is because they understand each other. So that leaves me with the first three.
While trust and understanding are important to a relationship, I think it is their faith in each other that truly powers their strength. I think that the word 'faith' nicely sums up
both the trust and understanding they have in much abundance of. I mean, what other word can nicely sum up Harry's actions during Valentine's day, where he understood Hermione's request was important and trusted her so implicitly as not to ask why he was needed in the first place? And I don't think I need to mention what Hermione has done, as she has done much more for Harry then he did for her (that blind, unappreciative git).
And it's not blind faith either. As shown throughout the books, there were plenty of times where they questioned the other, with the most recent one being the DoM incident. All of these times were times when one was irrationaly thinking, so the other has to set them straight. However, those only cover a very small fraction when compared to the times where they believed in the other. And I think that is the key here, H/Hr believe in each other barring the cases when the other is not thinking properly.
As I said before, H/Hr's faith in each other consists of the understanding and trust they have with each other. Also, another aspect that 'faith' covers is loyalty. (Which, btw
True Ship, should also be one of the choices up there.

) How can one person really have faith in another if they do not trust, understand, and is loyal to the other? Faith, IMO, is half of what love consists of, the other being physical attraction. It is faith that all couples should strive for because, once the attraction is gone, it is
the glue that keeps a couple together.
DragoonKain3 - who lurks back to his current addiction that is 'Master of Orion 3'.
As a side note, I really hope
Romulus Lupin posts his opinion on the matter. I always love his posts concerning subject matter such as this.