This paper aims to understand the role of most used centrality measures on the specific topics of shareholding networks, and to propose new measures for describing the emergence of market leaders. Data on companies and shareholdings are embedded into a weighted network. Both operational research and complex networks approaches are used. The former provides tools for unveiling paths of ownership and control that could not be evident at a first glance. The latter proposes the concept of centrality measure and offers a wide set of measures that add knowledge in understanding the relevance of nodes in the network. The combination of both approaches gives hints for understanding phenomena like tunnelling, that is relevant for the detection the response to market fluctuation due to financial instabilities. The present analysis also considers the response of the system under random and targeted attacks. The Italian Stock Market is examined as a case study.