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

TL;DR

This paper introduces a visualization method for large-scale production networks using an N-body simulation analogy, enabling hierarchical community detection in massive graphs efficiently.

Contribution

It presents a novel graph layout technique based on physical simulation, optimized for large networks, and demonstrates its effectiveness on manufacturing sector data.

Findings

Successfully visualized communities in a network of 10 million nodes

Achieved practical computation times with potential acceleration using specialized hardware

Identified hierarchical community structures in large-scale production data

Abstract

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.