Spatial Motifs for Device-to-Device Network Analysis in Cellular Networks

Device-to-device (D2D) communication is a promising approach to efficiently disseminate critical or viral information. Reaping the benefits of D2D-enabled networks is contingent upon choosing the optimal content dissemination policy subject to resource and user distribution constraints. In this paper, a novel D2D network analysis framework is proposed to study the impacts of frequently occurring subgraphs, known as motifs, on D2D network performance and to determine an effective content dissemination strategy. In the proposed framework, the distribution of devices in the D2D network is modeled as a Thomas cluster process (TCP), and two graph structures, the star, and chain motifs, are studied in the communication graph. Based on the properties of the TCP, the closed-form analytical expressions for the statistical significance, the outage probability, as well as the average throughput per device, are derived. The simulation results corroborate the analytical derivations and show the influence of different system topologies on the occurrence of motifs and the D2D system throughput. More importantly, the results highlight that, as the statistical significance of motifs increases, the system throughput will initially increase and then subsequently decreases. Hence, the network operators can obtain statistical significance regions for chain and star motifs that map to the optimal content dissemination performance. Furthermore, using the obtained regions and the analytical expressions for statistical significance, network operators can effectively identify which clusters of devices can be leveraged for D2D communications while determining the number of serving devices in each identified cluster.