I don't want to focus too much on one example, because I know the situation can vary.
When you say that you're looking for connections on Facebook, are you looking for links to content, such as a known phishing site seeking to extract financial information, or to people, such as business relationships that an individual guilty of suspicious transactions might have with a Facebook friend? How do you identify these people and their connections?
I don't see much difference between the police's investigative work and what your organization seems to be doing.