Geographic routing in social networks

Abstract

We live in a ''small world,'' where two arbitrary people are likely connected by a short chain of intermediate friends. With scant information about a target individual, people can successively forward a message along such a chain. Experimental studies have verified this property in real social networks, and theoretical models have been advanced to explain it. However, existing theoretical models have not been shown to capture behavior in real-world social networks. Here, we introduce a richer model relating geography and social-network friendship, in which the probability of befriending a particular person is inversely proportional to the number of closer people. In a large social network, we show that one-third of the friendships are independent of geography and the remainder exhibit the proposed relationship. Further, we prove analytically that short chains can be discovered in every network exhibiting the relationship.routing algorithms ͉ small worlds ͉ population networks ͉ rank-based friendships ͉ six degrees of separation

Optimal Routing for Multihop Social-Based D2D Communications in the Internet of Things

“…The rank-based model accounts for the majority of the friendships in the LiveJournal online community, as provided in [18]. Moreover, the work in [25] suggests that the model indeed guarantees smallworld properties, such that with geographical information only, a friendship chain with at most O(log 3 n) hops can be established between an arbitrary source node and a target node chosen uniformly at random from the whole population, where O denotes big O notation.…”

“…By applying these models in uniformly distributed networks, the capacity of a wireless network was studied in [19] in the context of social groups. The rank-based model states that the TP depends on both the geographic distance and the node density [18] and [20], which is more accurate than the distance-based model. In this paper, therefore, we apply the rank-based trust model in multi-hop D2D networks to derive a routing algorithm aimed at maximizing the trusted connectivity probability (T-CP), which is a very comprehensive model to select optimal path for multi-hop social-based D2D communications in the 5G IoT.…”

“…We consider path selection based on both CP and T-CP calculation for the cases of randomly located and fixed BSs. Furthermore, for the parameter of the rank-based model, β = 1 is assumed [18], [29]. Also, α = 4, I th = 5, and R th = 1 bit/s/Hz.…”

“…The nodes in each pair trust to each other by default, which is impractical. To overcome this problem, distance-based and rank-based trust models, which were proposed by [17] and [18], respectively, could be used to predict the trust probability (TP) for pair of nodes. By applying these models in uniformly distributed networks, the capacity of a wireless network was studied in [19] in the context of social groups.…”

“…In this paper, we considered the TP of D2D devices by using a rank-based trust model, which was proposed in [18] and [24] based on the analysis of daily experiences and real data traces from online social networks. Considering any two D2D devices D i and D i+1 , we define the rank of D i+1 with respect to D i as…”