I'd argue "friend of a friend" is strong transitivly because it's explicitly chosen by all parties involved.

Trust in a professional relation - a doctor, especially - is actually very strong, because of the professional requirements to be trustworthy, and the protections built into that (being held accountable by an organization and/or lawsuits).

"Family of friend" or "family of professional" isn't necessarily a strong relation for exactly the opposite reason, unless maybe the first-degree contract is vouching for the person.

There’s also a compounding effect. If multiple friends vouch for the same stranger that means something too.