Multilayer Network Approach to Dynamics of Japanese Interfirm Transaction Relations

To study the dynamics of complex networks, researchers may construct a network representing interactions (links) between basic entities (nodes) at every time step and combine the snapshot layers thus obtained to form a multilayer network by connecting common nodes that appear in the adjacent layers. The objective of this study is to carry out an empirical study on temporal change of Japanese interfirm transaction relations taking this promising approach, with an emphasis on community structure. To this end, the original node network is replaced by the corresponding link network in which the transaction relations play take part as nodes. We develop a new scheme to choose the optimum coupling strength between adjacent layers for detecting the most appropriate community structure of a multilayer network in an algorithmic manner. We determine that the size of the communities obeys a power-law distribution and dominant communities have specific characteristics with regard to evolutionary pattern and industrial categorization. We also illuminate the dynamics of the dominant communities using the optimized layout of the multilayered network embedded in three dimensional space.