New centrality indices, Bundle and Pivotal, were introduced (Aleskerov and Yakuba, Matrix-vector approach to construct generalized centrality indices in networks. Working paper WP7 series. Higher School of Economics Publ. House, 2020) to identify key vertices taking into account parameters of vertices and the influence of vertices on a vertex. However, the Bundle and Pivotal indices are constructed in such a way that they do not take into account directly the weights of arcs—important information about interaction among vertices in a network. We have constructed several new centrality indices that take into account this information as well. New centrality indices have been tested on real network models (rare earth compound export/import operations) and compared with the Bundle and Pivotal values.