Modeling and estimating the structure of D2D-based mobile social networks

Along with the explosive growth of mobile social network (MSN) users and the advent of device-to-device (D2D) communications, D2D-based MSN (D2D-MSN) has become a promising alternative for exchanging multimedia contents on-the-go. Although the complete structure of a D2D-MSN plays a key role in understanding its performance, such knowledge is not readily available due to the difficulty of collecting connectivity information from the vast amount of users. To model the structure, we define a D2D-MSN network that jointly captures the social connectivity over the MSN and the opportunistic D2D contacts among users. A random walk with self loop (RWSL) scheme that quickly converges to its stationary distribution is proposed to collect a subset of D2D-MSN nodes. An estimator is then introduced to obtain an unbiased estimate of the D2D-MSN graph's joint degree distribution, pi, j, from the set of visited nodes, leading to an unbiased RWSL scheme. The resulting estimate of pi, j can be used as a statistic for creating synthetic graph and generating functions for analyzing robustness of D2D-MSN. Numerical results show that the proposed unbiased RWSL converges faster to its stationary distribution, achieves higher joint degree distribution accuracy, and visits less number of nodes, compared to existing graph exploration schemes.