Table 1.
Time-averaged percentage of SCCN in each industry.
Fig 1.
Schematic image of the construction of the stock ownership (total) network and cross-shareholding (SCC-based) network.
Table 2.
Summary of network statistics for the SCCN from 2001 to 2023. The number of nodes , number of edges
, density ρ, average clustering coefficient
, and diameter D are shown. “I” and “F” denote the reports issues at the end of the interim period and the full fiscal year, respectively (e.g., 2001I denotes the interim period of 2001).
Fig 2.
Schematic representation of the bow-tie structure.
Fig 3.
Example of link structures with high and low authority/hub scores.
The authority score of node i increases when it shares shareholders with many other nodes (a) and decreases when it shares shareholders with fewer nodes (b). The hub score of node i increases when many other nodes are investing in the same companies as node i (c) and decreases when there are fewer such nodes (d).
Fig 4.
CCDF of (a) in-degree, (b) out-degree, (c) in-strength, and (d) out-strength.
The color varies from blue to red with time. The thick black dashed line in (b) and (d) represents a straight line of .
Fig 5.
Temporal changes in the ratios of nodes in the bow-tie structure components for the SCCN.
Error bars indicate 95% confidence intervals.
Fig 6.
Temporal changes in the ratios of nodes in the Core (top), OUT (middle), and IN (bottom) components of the bow-tie structure shown for two clusters that together include all industries, grouped based on similar temporal patterns.
Error bars indicate 95% confidence intervals.
Fig 7.
CCDF of (a) pa, (b) ph, (c) a, (d) h.
The color varies from blue to red with time. The thick black dashed line in (b) and (d) represents a straight line of .
Fig 8.
Visualization of the SCCN at five full years: (a) 2001, (b) 2006, (c) 2010, (d) 2018, and (e) 2023.
Node positions are arranged according to the bow-tie structure. The Core, OUT, and IN components are enclosed by purple dotted, orange dashed, and green solid lines, respectively. Node colors represent clusters identified using the Louvain method, and node sizes are scaled by the ph values at each time point.
Fig 9.
Temporal changes in Kendall’s rank correlation coefficients between pairs of network measures in the SCCN.
The subfigures are shown in descending order based on the average Kendall’s rank correlation coefficient (τ) over time. Gray shading represents the consecutive time points at which the 95% bootstrap confidence interval of the difference in Kendall’s τ excluded zero, indicating statistical significance at the 5% level. For example, panel (a) shows the temporal variation in the correlation between sout and h.
Fig 10.
Kendall’s rank correlation coefficients between pairs of network measures by industry.
The vertical axis represents pairs of network measures, and the horizontal axis represents industries. The heatmap shows the time-averaged Kendall’s rank correlation coefficients for each industry. The dendrogram is the result of hierarchical clustering using Euclidean distance and Ward’s method, where each industry was characterized by a 15-dimensional vector of Kendall’s rank correlation coefficients across all measure pairs.
Fig 11.
Temporal changes in the percentile ranks of sin, pa, a, sout, ph, and h for three representative clusters.
These clusters are selected examples from the seven clusters obtained via hierarchical clustering. Each subplot displays the time series of the average percentile rank for a specific network measure within one of these representative clusters. Industries are grouped in columns within each subplot based on the clustering result obtained using Euclidean distance and Ward’s method. Each industry is represented by a 276-dimensional vector comprising the percentile ranks of six network measures, sin, pa, a, sout, ph, and h, across 46 time points. Markers indicate the average percentile rank at each time point, and error bars represent the 45th to 55th percentile range. The left, center, and right subplots correspond to clusters respectively composed of banks, then information & communication, real estate, and services, and finally iron & steel and transportation equipment.
Fig 12.
Time averages of the percentile ranks of sin, pa, a, sout, ph, and h by each industry.
Each cell shows the time-averaged percentile rank of a network metric for a given industry. Rows correspond to industries, and columns to network metrics. The heatmap color scale ranges from blue (low percentile rank) to red (high percentile rank). The number following each industry name indicates the cluster to which the industry belongs based on the similarity of temporal variations in percentile ranks. These clusters were obtained by applying hierarchical clustering to 276-dimensional vectors (six network measures across 46 time points) for each industry, as visualized in S2 and S3 Figs. The black dashed lines in the heatmap denote the boundaries between clusters.