Influential nodes and anomalous topic activities in social networks using multivariate time series and topic modeling

It is important to understand the behavior within a social network, particularly excessive communications between nodes. Such excessive activities in a network provide an insight into the pattern of communication between nodes, which, in some cases, could lead to a fraudulent behavior. Scan statistics have been applied before to detect the excessive communications in email networks. However, they alone are not effective in revealing the dynamic relationships and progression of chatter as the scan statistics relate to the maximum of locality statistics. Here a multivariate time series model, vector autoregressive (VAR) model, has been developed and applied to the metadata of organization e-mails as a case study to detect a group of influential nodes and their dynamic relationship. Furthermore, we devise a new methodology, which utilizes the probabilistic topic model obtained from the e-mail content, scan statistics, and time series of maximum information flow. We demonstrate how the influential vertices obtained from the VAR model are connected with the anomalous topic activities. These methodologies would be highly useful in studying the excessive communications and anomalous topic activities in other dynamic networks, such as, twitter networks, telephone calls, scientific collaborations, and other social networks.