Large path losses of millimeter waves restrain the acceptance of 60 GHz technology in future networks. Directional antennas can be exploited in 60 GHz networks to mitigate the detrimental impact of fading. Employing fully directional antennas complicates the neighbor discovery process where each sector must be probed individually to discover neighbors located in that sector. In random scanning strategy, nodes select to-be-scanned sector randomly. In this letter, we analyze the minimum number of random sector scanning attempts during neighbor discovery process to have a non-isolated network. We present an analytical model to study the isolation probability defined as probability of having at least one isolated node in the network. Based on the isolation probability, we derive the minimum number of sector scanning attempts in a 60 GHz ad hoc network with arbitrary number of nodes. Although 60 GHz directional network is studied, this analysis is applicable to any directional wireless network.