Network of companies: an analysis of market concentration in the Italian stock market

In this paper we propose an adjustment to the Herfindahl–Hirschman concentration index for explicitly considering the role of the topology of financial economic networks on market concentration. The case study of the Italian stock market serves for outlining the relevance of the shareholding network in the measurement of effective concentration. Moreover, we deepen the analysis of the network comparing network centrality measures, that are a well known method for understanding the relative relevance of network nodes. The correlations among them show their relation, and the fact that none of them can completely substitute the information contained in the size of companies. Such analysis constitutes the base for randomized experiments aiming at understanding to which extent the topology of this financial economic network is constraining the market concentration, so we derive and comment the results on the maximum value of HH \(_{i}\) under the scale-free constraint. We also show the fragility of the network under random rewiring, both unconstrained and constrained by the network topology.