### Related Work  
This section summarizes recent work in the field of D2D communications utilizing social information of users. The survey papers, References [14, 15], review the current advancements in D2D communications and how social information can be used in the design of D2D systems. Social strength estimation techniques are proposed in Reference [16, 17]. Different energy efficient approaches for D2D communications are proposed in References [1, 13, 18, 19]. Multi-hop D2D communications are used in References [20, 21] and multicasting using D2D communications in Reference [22]. Social information of network users is used for relay selection to improve throughput of D2D communications in References [5, 7, 8, 12] and in our previous papers [9, 10, 11]. These papers and issues are reviewed in the remainder of this section. [PERSON] et al. [14] presented a brief overview of the standardization of D2D communication based on 3 GPP Release 12 and subsequent releases. They described the reference architecture for D2D communication, channel structure and features of D2D communications. Additionally, they discussed different challenges present in D2D communications and also highlighted some of the important areas of interaction between 5G and D2D communications. [PERSON] et al. [15] presented a survey on D2D communications focused on the utilization of social networks with the aim to explore and understand how the integration of social-awareness benefits D2D communications. Their survey identified social communities, social link/tie and social centrality as major social features of social network that can be used in D2D communications. Furthermore, they identified the key issues in D2D communications. The key issues are relay discovery and peer selection, communication mode selection, and spectrum resource allocation and management. Additionally, they summarized different proposed solutions using social networking. Social-interactions are now considered as a novel and imperative dimension in the design of communication systems [23]. Social relationship information of users can be used in D2D communications to reduce load on cellular systems [4]. The social relationship information obtained from online social networks are more detailed and complex in structure as compared to offline social networks [24]. [PERSON] et al. [16] proposed a method to estimate social tie strength in a network that consists of small number of users. They found that for a network having less than hundred users, social tie strength can be estimated using aggregated call duration. [PERSON] et al. [17] developed a social strength estimation which is based on interaction information of network users (e.g., communication, tagging) and similarities in account profile of users. The continuous-valued social strength estimated from the model is capable to provide link weights with higher autocorrelation, leading to improved accuracy in social trust estimation. However, in this paper we use Pareto distribution to model the social trust among users. This approach is also used in other studies [6; 12; 19]. Generally, mobile devices have limited storage capacity and are power constrained. In relay assisted D2D communication networks, relay devices which are unselfish might always forward data for others, and eventually run out of battery power. On the other hand, devices that are selfish might always use a relay to enhance their D2D communications, without forwarding data for others [5]. Therefore, it is necessary to design a D2D relay selection mechanism that motivates devices to relay data for others. [PERSON] et al. [18] proposed energy efficient medium access protocol for cooperative D2D communications that utilizes social information of users. They highlight some of the practical issues when social information is used in D2D communications. [PERSON] et al. [1] proposed energy efficient relay selection scheme for multi-relay D2D communications underlaying cellular systems.