These days when the word "relationship" is offered, the connotation is that of an intimate or personal relationship, as in "yeah, we're in a relationship now," meaning that they have become a couple, they're dating, they're seeing each other. Even facebook asks for one's "relationship status." Most younger people these days assume that's what you're talking about when you discuss relationships, what makes a good one, etc.
But there are other kinds of relationships too, and I think that's the broader scope that the OP is talking about. And they fall into 4 broad categories, each with sub categories of course, but still.
Family relationships
Friendships
Casual Relationships
Romantic or Intimate relationships
Trust, and an abundance of open, honest communication are foundational for me in any good relationship. I don't think you can establish trust and honesty without an abundance of communication.
I am slow to trust, and don't trust many people outside of my nuclear family and Ron and a couple of extremely close friends. That abundance of communication has to be present in any relationship as a first priority or I will never establish trust in the person, at least as far as family relationships and romantic relationships are concerned. I have friendships and casual relationships where the issue of trust and communication isn't as important. There's not a lot of heavy duty communication between us, and I don't particularly trust these people, but I don't NEED to, because our connection isn't particularly close or personal and there aren't really any situations that come up between us where there is a need for me to trust them.