As the rapid growth of mobile social net-works,mobile peer-to-peer(P2P)communications and mobile edge computing(MEC)have been developed to reduce the traffic load and improve the computation capacity of cellular networks.However,the stability of social network is largely ignored in the advances of P2P and MEC,which is related to the social relations between users.It plays a vital role in improving the efficiency and reliability of traffic offloading service.In this paper,we integrate an edge node and the nearby P2P users as a mobile P2P social network and introduce the problem of adaptive anchored(k,r)-core to maintain the stability of multiple mobile P2P networks.It aims to adaptively select and retain a set of critical users for each network,whose participation is critical to overall stability of the network,and allocate certain resource for them so that the maximum number of users of all networks will remain engaged and the traffic of cellular network can be minimized.We called the retained users as anchor vertices.To address it,we devise a peer-edge-cloud framework to achieve the adaptive allocation of resources.We also develop a similarity based onion layers anchored(k,r)-core(S-OLAK)algorithm to explore the anchor vertices.Experimental results based on a real large-scale mobile P2P data set demonstrate the effectiveness of our method.
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