Recently a lot of works have been investigating to find the tenuous groups, i.e., groups with few social interactions and weak relationships among members, for reviewer selection and psycho-educational group formation. However, the metrics (e.g., k-triangle, k-line, and k-tenuity) used to measure the tenuity, require a suitable k value to be specified which is difficult for users without background knowledge. Thus, in this paper we formulate the most tenuous group (MTG) query in terms of the group distance and average group distance of a group measuring the tenuity to eliminate the influence of parameter k on the tenuity of the group. To address the MTG problem, we first propose an exact algorithm, namely MTG-VDIS, which takes priority to selecting those vertices whose vertex distance is large, to generate the result group, and also utilizes effective filtering and pruning strategies. Since MTG-VDIS is not fast enough, we design an efficient exact algorithm, called MTG-VDGE, which exploits the degree metric to sort the vertexes and proposes a new combination order, namely degree and reverse based branch and bound (DRBB). MTG-VDGE gives priority to those vertices with small degree. For a large p, we further develop an approximation algorithm, namely MTG-VDLT, which discards candidate attendees with high degree to reduce the number of vertices to be considered. The experimental results on real datasets manifest that the proposed algorithms outperform existing approaches on both efficiency and group tenuity.