There is an etiquette to connecting with people we don't know (people in our 2nd and 3rd circles). In conversation with June and Valdis, I find out they know all kinds of people who are potentially interesting or important to me. I don't know how I fit into the world of these relationships they have built trust equity with.
It becomes a matter of courtesy, and core to our trust together, to let them know my intentions to connect with people in their close circles who they have revealed to me. They reveal their cherished connections because they trust that I will act in ways that honor their relationships and ours.
The best scenario is that they make the introductions they feel comfortable making. Of course, this can't apply when I have an accidental conversation with one of their close circle people, only realizing later that we have June's or Valdis' mutual trust in common.
In so-called "social network websites" where I can view someone's "736 closest friends" and start instantly connecting with/spamming them, I am violating introduction etiquette and risking the integrity and continuity of trust in all of the relationships involved.
Every introduction is an act of trust and trustworthiness. If I introduce you to one of my trusted friends or colleagues, it is in trust, that I am making a trustworthy introduction relative to the trust equity in our relationship.