The topology of shareholding networks

We study the statistical properties of the network of shareholding relationships in the Italian stock market (MIB) and in two US stock markets (NYSE and NASDAQ). The networks are found to be scale free a feature which doesn't seem to be in accord with classical theories of portfolio optimization. Several statistical properties differ across markets and allow for a classification. We introduce two quantities, HI and SI, analogous to in-degree and out-degree for weighted graphs. The distribution of HI and SI allow us to characterize from a statistical perspective the individual ownership concentration of stocks and the individual power of holders. They also suggest two different global pictures of the structure of the networks: the MIB seems characterized by medium size holders controlling separate subsets of stocks, while the US markets seem characterized by very large holders sharing control over subsets of stocks