Visualizing a large-scale structure of production network by N-body simulation

Our recent study of a nation-wide production network uncovered a community structure, namely how firms are connected by supplier-customer links into tightly-knit groups with high density in intra-groups and with lower connectivity in inter-groups. Here we propose a method to visualize the community structure by a graph layout based on a physical analogy. The layout can be calculated in a practical computation-time and is possible to be accelerated by a special-purpose device of GRAPE (gravity pipeline) developed for astrophysical N-body simulation. We show that the method successfully identifies the communities in a hierarchical way by applying it to the manufacturing sector comprising tenth million nodes and a half million edges. In addition, we discuss several limitations of this method, and propose a possible way to avoid all those problems

Shareholding Networks in Japan

The Japanese shareholding network existing at the end of March 2002 is studied empirically. The network is constructed from 2,303 listed companies and 53 non-listed financial institutions. We consider this network as a directed graph by drawing edges from shareholders to stock corporations. The lengths of the shareholder lists vary with the companies, and the most comprehensive lists contain the top 30 shareholders. Consequently, the distribution of incoming edges has an upper bound, while that of outgoing edges has no bound. The distribution of outgoing degrees is well explained by the power law function with an exponential tail. The exponent in the power law range is gamma=1.7. To understand these features from the viewpoint of a company's growth, we consider the correlations between the outgoing degree and the company's age, profit, and total assets.Comment: 10 pages, 4 figures, International Conference Science of Complex Networks: from Biology to the Internet and WWW (CNET2004

Labour Productivity Superstatistics

We discuss superstatistics theory of labour productivity. Productivity distribution across workers, firms and industrial sectors are studied empirically and found to obey power-distributions, in sharp contrast to the equilibrium theories of mainstream economics. The Pareto index is found to decrease with the level of aggregation, {\it i.e.}, from workers to firms and to industrial sectors. In order to explain these phenomenological laws, we propose a superstatistics framework, where the role of the fluctuating temperature is played by the fluctuating demand.Comment: 13 pages including figure