Detection of Stationarity and Local Dependence in Random Graphs Evolving by Preferential Attachment Model

The paper is devoted to the detection of stationarity and local dependence in directed random graphs evolving by the $\alpha$, $\beta$, and $\gamma$ schemes of the linear preferential attachment model proposed by Wan et al. (2020). To this end, the test proposed by Phillips and Loretan for detecting changes in the extreme value index for pairs of populations with regularly varying tails is utilized. The dynamics of the mean CC and the extremal index, which serves as a measure of local dependence applied to random graphs, are also examined. The exposition is illustrated through the change point detection in the real Flight network before, during and after COVID.