  The Japanese shareholding network at the end of March 2002 is studied. To
understand the characteristics of this network intuitively, we visualize it as
a directed graph and an adjacency matrix. Especially detailed features of
networks concerned with the automobile industry sector are discussed by using
the visualized networks. The shareholding network is also considered as an
undirected graph, because many quantities characterizing networks are defined
for undirected cases. For this undirected shareholding network, we show that a
degree distribution is well fitted by a power law function with an exponential
tail. The exponent in the power law range is gamma=1.8. We also show that the
spectrum of this network follows asymptotically the power law distribution with
the exponent delta=2.6. By comparison with gamma and delta, we find a scaling
relation delta=2gamma-1. The reason why this relation holds is attributed to
the local tree-like structure of networks. To clarify this structure, the
correlation between degrees and clustering coefficients is considered. We show
that this correlation is negative and fitted by the power law function with the
exponent alpha=1.1. This guarantees the local tree-like structure of the
network and suggests the existence of a hierarchical structure. We also show
that the degree correlation is negative and follows the power law function with
the exponent nu=0.8. This indicates a degree-nonassortative network, in which
hubs are not directly connected with each other. To understand these features
of the network from the viewpoint of a company's growth, we consider the
correlation between the degree and the company's total assets and age. It is
clarified that the degree and the company's total assets correlate strongly,
but the degree and the company's age have no correlation.
