I could start off about the three types of friendship outlined by Aristotle, but I don't think anyone want to hear that. So here's my viewpoint (relatable but more from my own thinking/experience leading to my thoughts).
One can view that everything is a "trade" of things. We are all stuck in the "algebra of wants and needs" and some people have more of one thing and we have more of the other. Therefore, it is arguable that all our friendships, even our relationships to family is a trade to get what we desire or need.
However, I think that leave out two major factors.
1. What the kind of self-interest bond. Two guys who became friends because they buy merchandise from each other is obviously very weak as those two have motives of making sure that they stay customers for each other. However, two friends that became friends because they like each other company and reason to be around is because they like the person around cannot be categorize as one and the same despite both project their self-interests and thus a wish for the other's well-being.
2. The type of people. A person who takes friendship more seriously will give more attention to friendship. It is arguably such a stance is a self-delusion/construct as there no absolute reason to stand by a friendship just for the sake of it (to be selfless, since it cannot take account of the self, it is almost always an irrational act). However, if one does, then ones does, thereby a selfless act. Thus, if one take friendship with heavy weight (meaning put large concern for their friends and etc.), they will act accordingly even if the exchange is only for the sake of the friendship (selfless act).
Is it always self-interested? Yes, because everything can always be broken down to a desire and that is always from within. However, what are the interests of the self prioritize and the value a person put into friendship makes alot of difference.
