In this paper, we propose a novel framework to study the problem of sequential detection of active substructures under the constraint of protection of edge-wise activity patterns. We begin by offering a definition of privacy within this framework as a means to a better interpretation of the constraints concerning our paper. We then formulate the novel problem of detecting active subgraphs from a given set of link-wise disjoint substructures. We show how such active graphs could be identified by querying with a series of feasible binary queries satisfying the constraint of protecting link-wise states over the detection period, a feat whose representation is further interpreted using vertex covering of subgraphs. Furthermore, we introduce the relationship between partial and complete vertex covering and the resulting breach of privacy imposed by the latter in our problem. A random coding approach is proposed to establish a sequential and non-adaptive binary search process whose average stopping time is analyzed based on both upper and lower bounds. Then the complexity of the method is calculated and shown to be efficient. Finally, the simulation results are provided to demonstrate the efficiency of proposed bounds.