With the rapid development of wireless communication technology and wide implementation of mobile devices, the distributed clouding has changed our lives. As one of the fundamental building blocks in distributed clouding, the connectivity problem on the user devices significantly impacts the quality of services provided by the distributed clouding. Different from the previous works that optimized the connections between the “strong” devices and the BS, this paper studies the connectivity problem on “weak” devices. We say a group of devices are strong devices if all of them can directly connect to the BS for sufficient long time without energy budget constraint. Otherwise, they are the weak devices, most of which cannot directly connect to the BS due to limited transmission power and hardware. Considering $n$ weak devices with uniform/non-uniform power settings, two approaches are designed in this paper to optimally connect all the weak devices to the BS within $O(n^{2})$ time slots. Since lots of mobile devices in our life are weak devices, it is believed that our connectivity approaches on the weak devices can extend the distributed clouding to some broader application scenarios.