  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.
