Measuring centrality metrics based on time-ordered graph in mobile social networks

One important issue in the study of Mobile Social Networks (MSNs) is to measure the centrality (importance) of nodes in networks. However, when measuring the centrality metrics in a certain time interval, the current studies in MSNs focus on analyzing static aggregation networks that do not change over time. Actually, network topology in MSNs is changing very rapidly, which is driven by natural social behavior of people. Therefore, it will not be accurate if the static aggregation network graph is used to measure centrality metrics in a period of time. In this paper, to solve this problem, we first introduce a time-ordered aggregation model, which reduces a dynamic network to a series of time-ordered networks. Then, we propose three particular time-ordered aggregation methods to measure the centrality of nodes in a certain period under two widely used centrality metrics, namely Betweenness centrality and Degree centrality. Finally, extensive trace-driven simulations are conducted to evaluate the performance of different aggregation methods. The results show that the time-ordered aggregation methods can measure the Betweenness and Degree centrality in a time interval more accurately than the Static Aggregation Method, and the Exponential Time-ordered Aggregation Method performs much better than other aggregation methods. Therefore, we recommend to use the Exponential Time-ordered Aggregation Method to measure centrality metrics in a certain time interval.