The impact of social groups on the capacity of wireless networks

The capacity of a wireless network with n nodes is studied when nodes communicate with one another in the context of social groups. Each node is assumed to have at least one local contact in each of the four directions of the plane in which the wireless network operates, and q(n) independent long-range social contacts forming its social group, one of which it selects randomly as its destination. The distance between source and the members of its social group follows a power-law distribution with parameter α, and communication between any two nodes takes place only within the physical transmission range; hence, source-destination communication takes place over multi-hop paths. The order capacity of such a composite network is derived as a function of the number of nodes (n), the social-group concentration (α), and the size of social groups (q(n)). It is shown that the maximum order capacity is attained when α ≥ 3, which makes social groups localized geographically, and that a wireless network can be scale-free when social groups are localized and independent of the number of nodes in the network, i.e., q(n) is independent of n.