Dynamic Graph Properties of Mobile Networks under Levy Walk Mobility

The performance of many algorithms in dynamic networks depends on the properties of the underlying graph representing the network. Since such a graph is inherently time-varying, quantifying the change in its structure is important for understanding the behavior of higher-layer network algorithms. In this paper, we study change in the dynamic graph structure of mobile wireless networks that evolve over time due to node mobility. We define several graph evolution metrics and evaluate them through extensive numerical simulations under Levy Walk mobility, which has been shown previously to have similarities to human mobility patterns. Based on the mean and distribution of these metrics, we obtain important insights into the properties of the evolving graph generated by Levy Walk mobility, and then compare the results to the Random Waypoint mobility model. Finally, we discuss the effects of the rate of graph change on the performance of network applications such as data routing and flooding. Our results suggest that the proposed metrics are viable for quantitatively measuring the magnitude of change in a sequence of evolving graphs.