Network of firms: an analysis of the relevance of integrated ownership in market concentration

In this work we aim to understand the role of the topology of financial economic networks on market concentration. We use the Herfindahl-Hirschman index (HHi) as a measure of market concentration, and we detect its maximum and minimum under the condition of scale-free shareholding data distribution, and power-law distribution of size of firms that have been estimated through empirical analyses. We show the relationship among positive correlation of size and the maximum and minimum value of HHi, depending on the parameter describing the scale-free network. The results show the relevance of the scale-free constraint on the values of HHi.