  This work deals with the issue of assessing the influence of a node in the
entire network and in the subnetwork to which it belongs as well, adapting the
classical idea of vertex centrality. We provide a general definition of
relative vertex centrality measure with respect to the classical one, referred
to the whole network. Specifically, we give a decomposition of the relative
centrality measure by including also the relative influence of the single node
with respect to a given subgraph containing it. The proposed measure of
relative centrality is tested in the empirical networks generated by collecting
assets of the $S\&P$ 100, focusing on two specific centrality indices:
betweenness and eigenvector centrality. The analysis is performed in a time
perspective, capturing the assets influence, with respect to the
characteristics of the analysed measures, in both the entire network and the
specific sectors to which the assets belong.
