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Networks of companies and branches in Poland

Anna Chmiel ,  Julian M. Sienkiewicz ,  Krzysztof Suchecki ,  Janusz A. Hołyst 

Warsaw University of Technology, Faculty of Physics and Cent.of Exc.for Complex Systems Research, Koszykowa 75, Warszawa 00-662, Poland

Abstract

Using a commercial data base 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 filter  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
 

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Presentation: Oral at 3 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Anna Chmiel
See On-line Journal of 3 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2007-09-17 12:58
Revised:   2009-06-07 00:44