Actor-Level Dynamicity: Its Distribution Analysis Eases Anomaly Detection in Longitudinal Networks

Different distributions have been observed across a wide variety of physical, biological, and man-made phenomena. For example, human height and blood pressure follow a normal distribution. Milk production by cows and the amount of rainfall follow a log-normal distribution. On the other side, the frequencies of words in most languages and family names best fit with the power-law distribution. Many real-life complex networks, such as author collaboration networks, also follow a power-law distribution. By considering four statistical distributions (i.e., normal, log-normal, exponential, and power-law), this paper first investigates the distribution of actor-level positional dynamicity in longitudinal networks. Positional dynamicity indicates the level of changes in actors' structural positions over time in a longitudinal network and has been used as a proxy for the actor-level dynamicity. The empirical investigation of two Facebook networks showed that actors' positional dynamicity values in longitudinal networks followed a power-law distribution. This power-law distribution did not change when different window sizes were used to explore the underlying longitudinal networks. This paper then explores how the power-law distribution of actor-level dynamicity values can be used for anomaly detection in longitudinal networks. The anomaly detection approach based on the power-law distribution of actors' positional dynamicity values revealed a superior application compared with a well-established anomaly detection approach. Finally, we discuss the implication of the power-law distribution of actor-level dynamicity in the context of other existing research problems related to complex networks.