Recently, integrated with the advanced communication technologies (e.g., 5G) and artificial intelligence (AI), mobile-edge intelligence (MEI) is regarded as the promising method to deal with the emerging challenges. Specifically, Device-to-Device (D2D) communications have been put forward to reduce the traffic pressure while extending cellular network capacity. However, the stability of the social network is important for the design of efficient and reliable traffic offloading strategy, which is often absent from the related work. Besides, most existing studies merely model the relation between a node pair as a binary or continuous value, neglecting the rich information between users. Moreover, many traditional models are conducted based on small-scale data sets or online Internet services, severely confining their applications in the D2D scenario. Thus, it is necessary to understand the network structure and select the key users to address the aforementioned challenges. In this article, we first propose a network representation model, named MPPT, to regard the multidimensional relations as a probability in a third-order (3-D) tensor space. Then, a mobile D2D social community is derived by integrating an edge base station (BS) and the nearby D2D users, and develop an anchored user selection algorithm to maintain the stability of multiple D2D social communities by choosing and retaining critical users adaptively under the limited network resources. Finally, we devise a probability-based onion layers anchored <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(k,r)$ </tex-math></inline-formula> -core (P-OLAK) algorithm to identify the anchor users. The large-scale data sets-based experimental results show the superiorities of the proposed methods.
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