# Temporal invariance of centrality correlations and hierarchical topology in evolving cross-shareholding networks in Japan (2001–2023)

## TL;DR

This study analyzes how the structure of cross-shareholding networks among Japanese companies evolved from 2001 to 2023, revealing stable patterns and shifts in influence.

## Contribution

The study introduces a long-term analysis of cross-shareholding networks using centrality correlations and hierarchical structures over 23 years.

## Key findings

- The core group of companies in the network decreased over time, while disconnected or one-way connected companies increased.
- Correlations among network measures like in-strength and PageRank remained stable, with notable shifts around 2010.
- Banks consistently showed low in-strength and high out-strength, but their hub influence declined over time.

## Abstract

In this study, we investigate the long-term evolution of the hierarchical structure and the stability of centrality correlations within Japan’s cross-shareholding networks. Using a 23-year dataset (2001–2023) of all listed Japanese companies, we conducted network analysis of semi-annually constructed networks of industrial sectors based on strongly connected components. To examine hierarchical structures, centrality distributions, and their intercorrelations, we applied bow-tie decomposition, PageRank, and the Hypertext-Induced Topic Selection (HITS) algorithm. The largest strongly connected component (the core group) decreased over time, whereas the number of companies that held shares in core members without being held in return (IN) or that remained entirely disconnected increased. Correlations among network measures exhibited temporal stability. The in-strength was positively correlated with both PageRank (pa), computed from the original directed network, and an authority score, whereas the out-strength was positively correlated with the Reversed PageRank (ph) computed from the reversed network and the hub score. A negative correlation was observed between pa and ph. The correlation between in-strength and out-strength shifted from negative to positive around 2010, suggesting stronger cross-shareholding ties among companies. Most industries exhibited network-measure correlations similar to those observed in the overall network. In contrast, transportation equipment showed no significant correlation between in-strength and the corresponding pa, which suggests that firms were less influenced despite holding significant inbound voting rights. The relative ranking of network measures across industries remained stable over time. Banks consistently ranked low for in-strength and high for out-strength. Although their ph ranks remained high, their hub score ranks decreased. These findings, such as the declining influence of banks and the rising centrality of the information & communication and real estate sectors, suggest that traditional firm-level or short-term monitoring may overlook systemic ownership structures. Periodic network-based monitoring can help to identify resilient and structurally influential firms or clusters.