## 1 Introduction  
With the rapid development of 5G, Internet of Things (IoT) and Artificial Intelligence (AI) in recent years, the degree of integration between the online social network and the entity has further enhanced. In this context, it is required to pay close attention to the human element in the information society. Identifying the cohesive structures, a fundamental task in Social Network Analysis (SNA), facilities to discover valuable hidden patterns and better understand and predict social networks. Formal Concept Analysis (FCA) [1], a mathematical tool based on lattice theory, is well applied to the research of identifying cohesive structures of the social network [2, 3]. Generally speaking, when FCA is used for social network analysis, the topological information of the social network is first used as the input of FCA. Then by the concept generation algorithm, the network structure is transformed into concept form which is extracted knowledge by FCA. The detailed process of how to use FCA in social networks analysis can refer to [2, 4]. In practice, the overwhelming size of the extracted knowledge, induced by formal concepts, limits its extensive use. How to understand concepts which represent structural topology is a key issue that affects the recognition accuracy. Considerable work [5, 6] has proved that the concept stability measure in the FCA theory community is useful for improving knowledge quality and revealing interesting patterns, which provides a theoretical basis for improving the recognition accuracy when FCA meets SNA. Indeed, concept stability, a bridge measure between FCA and SNA, is not only efficient for assessing the concept quality around the FCA [6], but also is widely used in numerous applications, e.g., community detection [7; 8], virtual machines scheduling in mobile edge computing [9], abnormal users detection in social networks [10]. For example, an illustration of the role of FCA and stability in identifying illegal users in social networks is presented in Figure 1. As shown in Figure 1a, abnormal users may deliver the same fake news to a certain online social network, which makes these users form a cohesive and illegal users group. Indeed, it is hidden common behaviors or characteristics that make these illegal users form relatively cohesive and isolated groups in social networks. Then, FCA can be used to identify various subgraph structures in social networks, but it cannot accurately identify the required structure. However, as shown in Figure 1c, the illegal user group can be accurately identified by using of stability measure. Nevertheless, the stability calculation is an NP-complete task [11; 12] which is the primary challenges in practical. To this end, in this paper, we focus on stability calculation to pave the way for the downstream tasks of the application of FCA in social network analysis. Although it is shown that the calculation of stability is an NP-complete problem, it is still attracting more and more attention as shown in the recent works [13; 14; 15; 16; 17; 18; 19; 20]. The dedicated literature could be roughly divided into two categories: computing approximate or exact values of stability. Most previous approaches rely on the whole structure of the concept lattice to compute approximate or exact values of stability. For example, jay's algorithm [16] of stability calculation requires browsing the entire concept lattice and summing over the stability already computed in lower levels. Obviously, this not only requires a lot of computing resources but also does not expect scalability when dealing with large concept lattices. A few accurate calculation algorithms, such as DFSP algorithm [18], start from calculating each concept separately and do not make full use of the potential knowledge in the concept lattice to speed up the algorithm.