We study the topological structure of the network of shareholding relationships in the Italian stock market (MIB) and in two US stock markets (NYSE and NASDAQ). The portfolio diversification and the wealth invested on the market by economical agents have been shown in our previous work to have all a power law behavior. However, a further investigation shows that the inner structure of the capital control network are not at all the same across markets. The shareholding network is a weighted graph, therefore we introduce two quantities analogous to in-degree and out-degree for weighted graphs which measure, respectively: the number of effective shareholders of a stock and the number of companies effectively controlled by a single holder. Combining the information carried by the distributions of these two quantities we are able to extract the backbone of each market and we find that while the MIB splits into several separated groups of interest, the US markets is characterized by very large holders sharing control on overlapping subsets of stocks. This method seems promising for the analysis of the topology of capital control networks in general and not only in the stock market.
