  Topological data analysis has recently been applied to the study of dynamic
networks. In this context, an algorithm was introduced and helps, among other
things, to detect early warning signals of abnormal changes in the dynamic
network under study. However, the complexity of this algorithm increases
significantly once the database studied grows. In this paper, we propose a
simplification of the algorithm without affecting its performance. We give
various applications and simulations of the new algorithm on some weighted
networks. The obtained results show clearly the efficiency of the introduced
approach. Moreover, in some cases, the proposed algorithm makes it possible to
highlight local information and sometimes early warning signals of local
abnormal changes.
