Incollection,
Networks of companies ans branches in Polnad
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
Using a commercial data basis we constructed a bipartite graph of companies and branches in Poland. The graph was transformed to create a companies network where a link means that two companies belong to at least one common trade and a link weight describes a number of common trades for a companies pair.
Similarly a branches network was constructed where nodes are branches and edges represent connections if at least one company belongs to the same branch. Corresponding link weights describe numbers of companies that are active in the same pair of branches. We have observed that a weight distribution is a power law function in the branches network while the distribution shows an exponential behavior in a certain range in the companies networks.
Using cutoffs of links weights we constructed networks with different filters levels and studied degree distributions for such networks. For a properly chosen cutoff values the degree distribution in the companies network is described by a power law with a characteristic exponent close one. Two regions of scaling can be observed for the branches network above some cutoff level. The Shannon entropy of degree distribution decays logarithmically as a function of the cutoff level. Both analyzed networks are assortative and their correlation coefficients increase with cutoff values of their link weights, for branches networks we observed maximum values of assortative for some regime of cutoff parameter
