Maintaining the network connectivity in mobile Multi-Robot Systems (MRSs) is a key issue in many robotic applications. In our view, the solution to this problem consists of two main steps: (i) making robots aware of the network connectivity; and (ii), making use of this knowledge to plan robots tasks without compromising connectivity. In this paper, the ad-hoc network connectivity as an abstraction that is independent from application issues. We propose a new distributed algorithm executing on individual robots to build the connectivity-awareness. The correctness and theoretical analysis of the proposed algorithm are given. We also show how our solution allows checking network bi-connectivity more efficiently than existing work and can be used, for example, during distributed control motion.