8. Conclusion
In this paper we defined the problem of friendship selection in the Social Network of Things, highlighting that if a SIoT is properly created then it can show the characteristics of a small world network and comply with the condition for network navigability Based on this knowledge, we proposed a model for a distributed friendship selection that relies on the Shapley-value. To this aim, the friendship selection process in the SIoT is mapped onto the coalition formation problem for a corresponding cooperative game. Based on two different utility functions, that meet the constraints for the system, the Shapley-value nicely models the importance of an object in the social IoT network and is thus used to set the friendship preferences. The resulting network navigability, in terms of average number of hops by using local peer search operations, is evaluated and compared with a standard solution where no limit on the friendships is set for the objects. The results showed how a better management of the number of friendships is obtained, at the expense of a negligible increase in the number of hops needed to reach a destination. A further extension for the implementation of the proposed solution that will be considered in our future research, is to consider enhancing aspects referring to the average path length. In particular, in our simulations we have considered all the possible pairs of nodes to be uniformly distributed over the network. However, it has been proven that friends share similar interests (bringing to the homophily phenomenon [52]), so that it is highly probable to find another node in the friends list or in the friend of a friend (FOAF) list, thus reducing the average path length among all the pairs of nodes. Node similarity for the routing operations has not been considered so far; indeed, in our simulations nodes try to reach their destination by using only information about the degree of their neighbors. However, external properties could be used to select the right nodes (among available friends) to which the desired service is requested. One of these properties is the profile of the friend involved (accounting for its trustworthiness and the type of relationship that links it to the requester).