The phrase "degree connections" refers to the number of people someone is connected to in a social network. It represents the extent of a person's relationships or contacts with others. Full definition
Growing my number of good quality connections, so that I have that many more second and third degree connections. (executivecareerbrand.com)
With any relational database, there is no efficient way to find 3rd degree connections. (onlinepersonalswatch.com)
Having a larger network means you have more 2nd degree connections which gives you the opportunity to view a lot more profiles. (careerintelligenceresumewriting.com)