Impact of Social Relation and Group Size in Multicast Ad Hoc Networks

This paper investigates the multicast capacity of static wireless social networks. We adopt the two-layer network model, which includes the social layer and the networking layer. In the social layer, the social group size of each source node is modeled as power-law distribution. Moreover, the rank-based model is utilized to describe the relation between source and destinations in the networking layer. Based on the two-layer network model, the probability density function (PDF) of the destination positions is analyzed and verified by numerical simulation, which is different from the traditional ad hoc networks. According to the PDF, the bound of the network capacity is derived, and we propose a Euclidean minimum-spanning-tree-based transmission scheme, which is proved to achieve the order of capacity bound for most cases. Finally, the capacity of social networks is compared to the traditional multicast ad hoc networks, which indicates that the capacity scaling performs better in social networks than traditional ones. To our best knowledge, this is the first work of analyzing the impact on the capacity of social relation and group size in multicast ad hoc networks for the rank-based model.