Organisational Social Capital in European Board Interlocks, 2022
Group I: MikołajK Stanisław rzyżanek, Artem Afonin, Brianna-Alecsandra Manta, Dongliang Zhang
1 November 2026
This report asks a simple question. When large European firms are linked because they share directors, does that network position work as organisational social capital, and does it show up in profitability?
The course brief allows either individual social capital (directors) or organisational social capital (firms). We study firms. A tie is a board interlock in 2022: two companies are linked when at least one person sits on both boards. We treat that tie as relational social capital, measure it with standard network statistics, and compare high- and low-capital firms on return on assets.
needed_pkgs <- c("igraph", "knitr")
missing_pkgs <- needed_pkgs[!vapply(needed_pkgs, requireNamespace, logical(1), quietly = TRUE)]
if (length(missing_pkgs) > 0) {
stop(paste("Install these packages before knitting:", paste(missing_pkgs, collapse = ", ")))
}
library(igraph)
library(knitr)1 Team members of Group I
| Name | Student ID |
|---|---|
| Mikołaj Stanisław Krzyżanek | 471762 |
| Artem Afonin | 486766 |
| Brianna-Alecsandra Manta | 488597 |
| Dongliang Zhang | 488390 |
2 Data loading and initialisation
Seven files were provided. Three enter the analysis. The others describe directors (shared university, shared graduation year, shared previous employment, and director attributes). They fit an individual-level design, which we do not pursue here.
| File | Role in this report |
|---|---|
1. companies interlocks one-mode network 2022.csv |
Binary company-by-company interlock matrix |
5. companies_covariates.csv |
Sector, country, profitability, employment, assets |
7. director_company_network_2022.csv |
Director-by-company seats; used to check what an interlock is |
2, 3, 4, 6 |
Director networks and attributes; not used |
The matrix files are semicolon-separated. The first column holds row names. The diagonal of the interlock matrix is a self-entry, so we set it to zero before any network statistic is computed. A firm is not tied to itself.
矩阵文件以分号分隔。第一列包含行名。互锁矩阵的对角线元素为自变量，因此在计算任何网络统计数据之前，我们将其设置为零。公司之间不存在关联。
data_dir <- "."
needed_files <- c(
"1. companies interlocks one-mode network 2022.csv",
"5. companies_covariates.csv",
"7. director_company_network_2022.csv"
)
missing_files <- needed_files[!file.exists(file.path(data_dir, needed_files))]
if (length(missing_files) > 0) {
stop(paste("Missing data files:", paste(missing_files, collapse = ", ")))
}
read_matrix <- function(file_name) {
dat <- read.csv(
file.path(data_dir, file_name),
sep = ";",
check.names = FALSE,
row.names = 1,
stringsAsFactors = FALSE
)
mat <- as.matrix(dat)
storage.mode(mat) <- "numeric"
mat
}
interlock_raw <- read_matrix("1. companies interlocks one-mode network 2022.csv")
if (!isSymmetric(interlock_raw)) {
stop("The interlock matrix is not symmetric.")
}
if (!identical(rownames(interlock_raw), colnames(interlock_raw))) {
stop("Row names and column names of the interlock matrix differ.")
}
interlock <- interlock_raw
diag(interlock) <- 0
firms <- read.csv(
file.path(data_dir, "5. companies_covariates.csv"),
sep = ";",
check.names = FALSE,
stringsAsFactors = FALSE
)
if (!identical(firms[["Company name (Orbis)"]], rownames(interlock))) {
firms <- firms[match(rownames(interlock), firms[["Company name (Orbis)"]]), ]
}
if (any(is.na(firms[["Company name (Orbis)"]]))) {
stop("Some firms in the interlock matrix have no covariates.")
}
seats <- read_matrix("7. director_company_network_2022.csv")
if (!identical(colnames(seats), colnames(interlock))) {
stop("Company columns in the director-company file do not match the interlock file.")
}
# One-mode projection: number of shared directors. The supplied interlock
# file keeps only the presence of a shared director.
shared_directors <- t(seats) %*% seats
diag(shared_directors) <- 0
projection_matches <- all((shared_directors > 0) == (interlock > 0))
if (!projection_matches) {
stop("The binary interlock file does not match the director-company projection.")
}
firm <- data.frame(
company = rownames(interlock),
sector = firms[["Stoxx Sector"]],
country = firms[["Country code (Orbis)"]],
roa = firms[["Returns_On_Assets_%_2022"]],
ros = firms[["Returns_on_Sales_%_2022"]],
ln_employees = firms[["ln_nr_of_employees_2022"]],
ln_assets = firms[["ln_total_assets_thousands_USD_2022"]],
board_size = as.numeric(colSums(seats)),
stringsAsFactors = FALSE
)g <- graph_from_adjacency_matrix(interlock, mode = "undirected", diag = FALSE)
if (any(which_loop(g))) {
stop("Self-loops remained in the graph.")
}
V(g)$sector <- firm$sector
V(g)$country <- firm$country
V(g)$roa <- firm$roa
V(g)$ros <- firm$ros
V(g)$ln_employees <- firm$ln_employees
V(g)$ln_assets <- firm$ln_assets
V(g)$board_size <- firm$board_size
# Access: how many other firms share a director.
# Brokerage: how often the firm sits on shortest paths between other firms.
# Closure: how often the firm's partners are also tied to each other.
V(g)$degree <- degree(g)
V(g)$betweenness <- betweenness(g, normalized = TRUE)
V(g)$clustering <- transitivity(g, type = "local")
V(g)$constraint <- constraint(g)
firm$degree <- V(g)$degree
firm$betweenness <- V(g)$betweenness
firm$clustering <- V(g)$clustering
firm$constraint <- V(g)$constraint
# High access starts at the upper quartile (degree 6). Low access is the
# lower quartile (degree 0 to 2). The middle band is everyone else.
firm$access_group <- ifelse(
firm$degree >= 6, "High (degree 6+)",
ifelse(firm$degree <= 2, "Low (degree 0-2)", "Medium (degree 3-5)")
)
firm$access_group <- factor(
firm$access_group,
levels = c("Low (degree 0-2)", "Medium (degree 3-5)", "High (degree 6+)")
)
upper <- upper.tri(shared_directors)
tie_weight <- shared_directors[upper][interlock[upper] == 1]
share_single_director <- mean(tie_weight == 1)
comp <- components(g)
giant_id <- which.max(comp$csize)
in_giant <- comp$membership == giant_idThe director-company file reproduces the binary interlock file exactly, so every tie in the analysis is a shared board seat. Most of those ties are thin.
init_summary <- data.frame(
Item = c(
"Firms",
"Directors listed in the seat file",
"Directors with at least one seat here",
"Directors who sit on two or more of these boards",
"Undirected interlocks",
"Interlocks carried by one director",
"Density",
"Components",
"Firms in the largest component",
"Isolates",
"Mean degree",
"Firms missing ROA"
),
Value = c(
vcount(g),
nrow(seats),
sum(rowSums(seats) >= 1),
sum(rowSums(seats) >= 2),
ecount(g),
sprintf("%.1f%%", 100 * share_single_director),
sprintf("%.3f", edge_density(g)),
comp$no,
max(comp$csize),
sum(degree(g) == 0),
sprintf("%.2f", mean(degree(g))),
sum(is.na(firm$roa))
),
stringsAsFactors = FALSE
)
kable(init_summary, caption = "Network after initialisation.")| Item | Value |
|---|---|
| Firms | 143 |
| Directors listed in the seat file | 499 |
| Directors with at least one seat here | 429 |
| Directors who sit on two or more of these boards | 249 |
| Undirected interlocks | 277 |
| Interlocks carried by one director | 90.6% |
| Density | 0.027 |
| Components | 11 |
| Firms in the largest component | 132 |
| Isolates | 9 |
| Mean degree | 3.87 |
| Firms missing ROA | 1 |
Sub-conclusion from the data build: the object of analysis is a sparse binary graph of 143 firms. An interlock almost always means one shared person, so these are thin bridges between organisations rather than thick, multi-director bonds.
3 Data analysis
3.1 Access and brokerage are the two forms of social capital we measure
Social capital, in the sense used here, is the value of relationships (Lin). For an organisation, the structural part of that value sits in the board network (Nahapiet and Ghoshal). Three ideas from network theory say what the value might be.
- Access. A firm with more interlocks can reach more of the corporate elite. Coleman treats a dense neighbourhood as closure: partners know one another, which supports trust and a shared line. We measure the volume of access with degree. We measure closure, where it is defined, with local clustering.
- Brokerage. Burt’s structural-hole argument says the advantage is different. A firm gains when it links contacts who are not linked to each other, because it hears non-redundant news and can coordinate across groups. We measure brokerage with normalised betweenness. Burt’s constraint is the mirror image: high constraint means the neighbourhood is closed and redundant.
- Why either form could help. Resource-dependence theory treats the board as a tool for managing dependence on the outside world (Pfeffer and Salancik). Useem’s “inner circle” treats multiple board seats as the channel through which a corporate elite shares information and class-wide interests. Both stories predict that a central position is an asset. They do not predict that the asset must appear as a higher return on assets in one year.
Degree and betweenness move together in this network, but they are not the same score. The firms far to the right of the plot have many partners. The firms high on the plot sit on more paths. Nestlé is extreme on both. A firm can have several interlocks and still be a poor broker if those partners already lie in one cluster.
plot(
firm$degree, firm$betweenness,
xlab = "Degree (number of interlocked firms)",
ylab = "Normalised betweenness",
main = "Access and brokerage rise together, but they are not the same",
pch = 19, col = rgb(0.15, 0.35, 0.55, 0.75)
)
abline(lm(betweenness ~ degree, data = firm), col = "#b2182b", lwd = 2)
cor_deg_btw <- cor(firm$degree, firm$betweenness)
cor_test_deg_btw <- cor.test(firm$degree, firm$betweenness)
top_both <- firm[order(-firm$degree, -firm$betweenness), c("company", "degree", "betweenness", "constraint", "country")]
kable(
head(top_both, 8),
digits = 3,
row.names = FALSE,
caption = "Eight firms with the most interlocks. Constraint is Burt's measure; lower means a less redundant neighbourhood. It is undefined for isolates and is missing nowhere in this top group."
)| company | degree | betweenness | constraint | country |
|---|---|---|---|---|
| NESTLE S.A. | 13 | 0.188 | 0.095 | CH |
| DANONE | 12 | 0.080 | 0.135 | FR |
| ORANGE | 12 | 0.055 | 0.134 | FR |
| L’OREAL | 11 | 0.069 | 0.120 | FR |
| HENKEL AG & CO. KGAA | 10 | 0.050 | 0.161 | DE |
| SIEMENS AG | 9 | 0.064 | 0.165 | DE |
| SANOFI | 9 | 0.022 | 0.163 | FR |
| SCHNEIDER ELECTRIC SE | 8 | 0.080 | 0.130 | FR |
The correlation between degree and betweenness is 0.79. Local clustering in the whole graph is 0.15, so closed triangles are present but not the typical pattern. About 91 percent of interlocks are a single shared director. In Granovetter’s language, the bridges between firms are weak ties: one person, not a thick bond.
Sub-conclusion: organisational social capital here has two measurable parts, access (degree) and brokerage (betweenness). The centre of the network holds both. Closure is the exception, not the structure of the elite.
3.3 Larger firms, and larger boards, hold more of it
If interlocks were mainly a strategic investment, size would not dominate the pattern. It does. Degree correlates with log employment at 0.44 and with log assets at 0.27. Board size correlates with degree at 0.82. A larger board offers more chances that one member also sits elsewhere. Part of what we call access is therefore a by-product of scale.
Sector differences are real but smaller than this size gradient. Consumer, food, automobile, and telecom firms sit a bit higher. Basic resources, energy, and real estate sit lower. Several sectors have very few firms, so those means are descriptive, not a ranking to over-interpret.
plot(
firm$ln_employees, firm$degree,
xlab = "Log number of employees, 2022",
ylab = "Degree",
main = "Larger employers have more board interlocks",
pch = 19, col = rgb(0.15, 0.35, 0.55, 0.75)
)
abline(lm(degree ~ ln_employees, data = firm), col = "#b2182b", lwd = 2)
sector_mean <- sort(tapply(firm$degree, firm$sector, mean))
sector_n <- tapply(firm$degree, firm$sector, length)
sector_labels <- paste0(names(sector_mean), " (n=", sector_n[names(sector_mean)], ")")
old_par <- par(mar = c(4.2, 16, 3, 1))
barplot(
sector_mean,
horiz = TRUE,
names.arg = sector_labels,
las = 1,
cex.names = 0.72,
xlab = "Mean degree",
main = "Mean interlocks by sector",
col = "#4c78a8",
border = NA
)
Sub-conclusion: the firms that look rich in relational social capital are, first, large firms with large boards. Sector colours the pattern. It does not replace size.
3.4 The ties stay inside countries
Homophily is the tendency of similar actors to tie to each other. Here the relevant similarity is the country of the firm, not its industry. National business systems still organise European corporate elites: careers, ownership, and board recruitment are more national than the product market is.
Two comparisons make the point. Country assortativity is high. Sector assortativity is close to zero. We also compare the share of ties that stay inside the same country, or the same sector, with the share we get by shuffling labels while keeping the graph fixed (1,000 permutations).
el <- as_edgelist(g, names = FALSE)
tie_share <- function(labels) {
mean(labels[el[, 1]] == labels[el[, 2]])
}
obs_country <- tie_share(V(g)$country)
obs_sector <- tie_share(V(g)$sector)
set.seed(2022)
perm_country <- replicate(1000, tie_share(sample(V(g)$country)))
perm_sector <- replicate(1000, tie_share(sample(V(g)$sector)))
assort_country <- assortativity_nominal(
g, as.integer(factor(V(g)$country)),
directed = FALSE
)
assort_sector <- assortativity_nominal(
g, as.integer(factor(V(g)$sector)),
directed = FALSE
)
homophily_tab <- data.frame(
Attribute = c("Country", "Sector"),
Assortativity = c(assort_country, assort_sector),
Observed_within_tie_share = c(obs_country, obs_sector),
Mean_share_under_label_shuffle = c(mean(perm_country), mean(perm_sector)),
Permutation_p = c(mean(perm_country >= obs_country), mean(perm_sector >= obs_sector)),
stringsAsFactors = FALSE
)
kable(
homophily_tab,
digits = 3,
caption = "Homophily. The permutation p-value is the share of label shuffles with a within-tie share at least as large as the observed share."
)| Attribute | Assortativity | Observed_within_tie_share | Mean_share_under_label_shuffle | Permutation_p |
|---|---|---|---|---|
| Country | 0.446 | 0.538 | 0.123 | 0.000 |
| Sector | 0.026 | 0.119 | 0.087 | 0.041 |
old_par <- par(mfrow = c(1, 2), mar = c(4.2, 4.2, 3, 1))
barplot(
rbind(
c(obs_country, obs_sector),
c(mean(perm_country), mean(perm_sector))
),
beside = TRUE,
names.arg = c("Country", "Sector"),
ylim = c(0, 0.7),
ylab = "Share of ties within the attribute",
main = "Ties stay in-country",
col = c("#4c78a8", "#d9d9d9"),
border = NA,
legend.text = c("Observed", "Label shuffle"),
args.legend = list(bty = "n", x = "topright")
)
country_mean <- sort(tapply(firm$degree, firm$country, mean))
barplot(
country_mean,
las = 2,
ylab = "Mean degree",
main = "France and Germany sit higher",
col = "#4c78a8",
border = NA
)
About 54 percent of interlocks join two firms from the same country, against about 12 percent under a random labelling. The same comparison for sector is 12 percent observed against 9 percent expected. France (mean degree 6.0, n = 25) and Germany (4.6, n = 22) are the dense national cores. Britain has the most firms in the sample (n = 29) but a lower mean degree (3.1).
The picture of the largest component shows the same fact. Node colour is country, for the five countries with the most firms. Node area grows with degree. Same-coloured nodes cluster, and the largest nodes are not spread evenly across colours.
g_giant <- induced_subgraph(g, vids = which(in_giant))
core_countries <- c("FR", "DE", "GB", "CH", "NL")
giant_country <- ifelse(V(g_giant)$country %in% core_countries, V(g_giant)$country, "Other")
country_colours <- c(
FR = "#2166ac",
DE = "#b2182b",
GB = "#ef8a62",
CH = "#762a83",
NL = "#1b7837",
Other = "#bdbdbd"
)
set.seed(2022)
layout_giant <- layout_with_fr(g_giant, niter = 500)
plot(
g_giant,
layout = layout_giant,
vertex.size = 3 + 11 * degree(g_giant) / max(degree(g)),
vertex.color = country_colours[giant_country],
vertex.frame.color = NA,
vertex.label = NA,
edge.color = rgb(0.35, 0.35, 0.35, 0.35),
edge.width = 0.6,
main = "Largest component: colour is country, size is degree"
)
legend(
"topright",
legend = names(country_colours),
col = country_colours,
pch = 19,
pt.cex = 1.4,
bty = "n",
cex = 0.85
)
Sub-conclusion: relational social capital in this sample is a national elite resource that crosses industry. French and German firms are the clearest high-capital groups. A shared sector does little to create a tie.
3.5 Profitability does not follow social capital in 2022
The advantage claimed for social capital is better access to information, influence, and coordination, which might raise performance. The outcomes we can see are return on assets and return on sales in 2022. Deutsche Telekom has no ROA figure, so the ROA calculations use 142 firms. Four firms have no ROS figure.
The scatters are the result. A line fitted to either cloud is flat. High-degree firms are not the high-ROA firms. The same is true for brokerage. The grouped comparison asks the question in the form the brief suggests, high versus low social capital. Profit does not rise as we move from the low group to the high group.
roa_ok <- !is.na(firm$roa)
old_par <- par(mfrow = c(1, 2), mar = c(4.2, 4.2, 3, 1))
plot(
firm$degree[roa_ok], firm$roa[roa_ok],
xlab = "Degree",
ylab = "Return on assets, 2022 (%)",
main = "Access and ROA",
pch = 19, col = rgb(0.15, 0.35, 0.55, 0.75)
)
abline(lm(roa ~ degree, data = firm), col = "#b2182b", lwd = 2)
plot(
firm$betweenness[roa_ok], firm$roa[roa_ok],
xlab = "Normalised betweenness",
ylab = "Return on assets, 2022 (%)",
main = "Brokerage and ROA",
pch = 19, col = rgb(0.15, 0.35, 0.55, 0.75)
)
abline(lm(roa ~ betweenness, data = firm), col = "#b2182b", lwd = 2)
cor_degree_roa <- cor(firm$degree, firm$roa, use = "complete.obs")
cor_btw_roa <- cor(firm$betweenness, firm$roa, use = "complete.obs")
cor_degree_ros <- cor(firm$degree, firm$ros, use = "complete.obs")
cor_btw_ros <- cor(firm$betweenness, firm$ros, use = "complete.obs")
p_degree_roa <- cor.test(firm$degree, firm$roa)$p.value
p_btw_roa <- cor.test(firm$betweenness, firm$roa)$p.value
# Residual association after the two scale measures that create degree.
size_ok <- complete.cases(firm[, c("degree", "betweenness", "roa", "board_size", "ln_assets")])
resid_degree <- residuals(lm(degree ~ board_size + ln_assets, data = firm[size_ok, ]))
resid_btw <- residuals(lm(betweenness ~ board_size + ln_assets, data = firm[size_ok, ]))
resid_roa <- residuals(lm(roa ~ board_size + ln_assets, data = firm[size_ok, ]))
partial_degree_roa <- cor(resid_degree, resid_roa)
partial_btw_roa <- cor(resid_btw, resid_roa)
connected <- firm$degree >= 2 & !is.na(firm$roa) & !is.na(firm$clustering)
cor_closure_roa <- cor(firm$clustering[connected], firm$roa[connected])
profit_cor <- data.frame(
Association = c(
"Degree and ROA",
"Betweenness and ROA",
"Degree and ROS",
"Betweenness and ROS",
"Degree and ROA, residual of board size and assets",
"Betweenness and ROA, residual of board size and assets",
"Local clustering and ROA (degree at least 2)"
),
Correlation = c(
cor_degree_roa, cor_btw_roa, cor_degree_ros, cor_btw_ros,
partial_degree_roa, partial_btw_roa, cor_closure_roa
),
stringsAsFactors = FALSE
)
kable(profit_cor, digits = 3, caption = "Linear association between social-capital measures and 2022 profitability.")| Association | Correlation |
|---|---|
| Degree and ROA | -0.029 |
| Betweenness and ROA | 0.020 |
| Degree and ROS | -0.027 |
| Betweenness and ROS | -0.025 |
| Degree and ROA, residual of board size and assets | -0.054 |
| Betweenness and ROA, residual of board size and assets | 0.023 |
| Local clustering and ROA (degree at least 2) | -0.029 |
Degree and ROA correlate at -0.029 (p = 0.73). Betweenness and ROA correlate at 0.020 (p = 0.81). Holding board size and assets constant does not uncover a hidden positive link. Closure, among firms with at least two partners, is also unrelated to ROA in any substantial way.
The regression puts the same variables in one equation. The degree and betweenness coefficients are imprecise and are not distinguishable from zero. Log assets is the term that moves, and it moves negative: in this particular year, larger balance sheets are not higher-ROA balance sheets. Log employment points the other way once assets are included, which is a size composition effect, not a network effect. Either way, the model explains little of the variation in ROA. Social capital is not the missing explanatory piece.
m_access <- lm(roa ~ degree + board_size + ln_assets, data = firm)
m_broker <- lm(roa ~ betweenness + board_size + ln_assets, data = firm)
m_both <- lm(roa ~ degree + betweenness + board_size + ln_assets + ln_employees, data = firm)
coef_frame <- function(model) {
tab <- as.data.frame(summary(model)$coefficients)
tab$Term <- rownames(tab)
tab <- tab[, c("Term", "Estimate", "Std. Error", "t value", "Pr(>|t|)")]
rownames(tab) <- NULL
tab
}
kable(coef_frame(m_access), digits = 3, caption = paste0("ROA on degree, board size, and log assets. R-squared = ", sprintf("%.3f", summary(m_access)$r.squared), "."))| Term | Estimate | Std. Error | t value | Pr(>|t|) |
|---|---|---|---|---|
| (Intercept) | 21.236 | 8.273 | 2.567 | 0.011 |
| degree | -0.209 | 0.331 | -0.632 | 0.528 |
| board_size | 0.243 | 0.286 | 0.850 | 0.397 |
| ln_assets | -0.871 | 0.488 | -1.786 | 0.076 |
kable(coef_frame(m_both), digits = 3, caption = paste0("ROA on both social-capital scores plus scale. R-squared = ", sprintf("%.3f", summary(m_both)$r.squared), "."))| Term | Estimate | Std. Error | t value | Pr(>|t|) |
|---|---|---|---|---|
| (Intercept) | 20.491 | 8.166 | 2.509 | 0.013 |
| degree | -0.539 | 0.400 | -1.345 | 0.181 |
| betweenness | 32.735 | 34.409 | 0.951 | 0.343 |
| board_size | 0.163 | 0.284 | 0.573 | 0.568 |
| ln_assets | -1.568 | 0.569 | -2.758 | 0.007 |
| ln_employees | 1.303 | 0.560 | 2.326 | 0.022 |
group_roa <- aggregate(roa ~ access_group, data = firm, function(x) {
c(n = sum(!is.na(x)), mean = mean(x, na.rm = TRUE), median = median(x, na.rm = TRUE))
})
group_roa <- data.frame(
Access_group = group_roa$access_group,
n = group_roa$roa[, "n"],
Mean_ROA = group_roa$roa[, "mean"],
Median_ROA = group_roa$roa[, "median"]
)
kable(
group_roa,
digits = 2,
caption = "ROA by access group. High access is degree of 6 or more. One high-access firm, Deutsche Telekom, has no ROA and drops out of this table."
)| Access_group | n | Mean_ROA | Median_ROA |
|---|---|---|---|
| Low (degree 0-2) | 53 | 5.87 | 5.92 |
| Medium (degree 3-5) | 52 | 7.38 | 6.88 |
| High (degree 6+) | 37 | 5.97 | 5.74 |
boxplot(
roa ~ access_group,
data = firm,
ylab = "Return on assets, 2022 (%)",
xlab = NULL,
main = "ROA is similar across low, medium, and high access",
col = c("#d9d9d9", "#9ecae1", "#4c78a8"),
outline = FALSE
)
This is a cross-section of one year. It does not say that interlocks never help, or that they never follow from past success. It says that, among these firms in 2022, the firms with more access or more brokerage are not the more profitable firms. Mizruchi’s review of interlock research is consistent with that modesty: shared directors are a real channel of information and influence, and the performance evidence is mixed.
Mean ROA is 5.9 percent in the low group, 7.4 percent in the medium group, and 6.0 percent in the high group. The medium group is a bit higher. The high-access firms are not.
Sub-conclusion: high and low social-capital firms are easy to tell apart in the network, and hard to tell apart in 2022 profitability. The advantage we can document is positional. It is not a return-on-assets premium.
4 Conclusion
Organisational social capital, in this study, is the board-interlock position of a firm. Access is the number of other firms reached through shared directors. Brokerage is the extent to which the firm lies between others. Both are standard network readings of the same idea: relationships are a resource because they carry information, reputation, and a way to coordinate (Lin; Burt; Useem).
The measures support that idea as a description of the elite, and they do not support it as a profit formula for 2022.
- The resource is real and unequal. A giant component holds most firms, degree is skewed, and brokerage is more skewed still. Nestlé, Danone, Orange, L’Oréal, and a short list of peers occupy the centre. Nine firms have no interlock at all.
- The resource follows scale. Larger employers and larger boards have more interlocks. Degree and board size move almost in lockstep, so a raw degree ranking partly restates organisational size.
- The resource is national. More than half of all ties stay inside one country, far above chance. Sector does not organise the network. France and Germany are the high-capital cores. This is homophily at the level of business systems, not an industry club.
- The resource does not separate profitable firms from less profitable ones in this year. Correlations of degree, betweenness, and local clustering with ROA and ROS are about zero, including after board size and assets are held constant. The medium-access group is not worse off than the high-access group.
The advantage of this social capital is therefore membership in a national corporate elite: more contacts, and a better chance of sitting between contacts. That is the advantage Burt and Useem describe. It is a different claim from “central firms earn a higher return on assets”, and the 2022 numbers do not support that second claim. Interlocks may stabilise access and status even when they do not raise the accounting return. They may also be costly, ceremonial, or a consequence of size rather than a cause of profit.
The limits of the evidence are straightforward. The design is one cross-section, so it cannot separate cause from effect. Profitability is a single year, and 2022 was a particular macroeconomic year. Ties are binary even though a few firm pairs share more than one director. Countries other than France, Germany, Britain, Switzerland, and the Netherlands have few firms. One firm is missing ROA. A later design could follow the same firms over time, or turn to the director files and ask the individual-level questions the brief also allows: brokerage versus closure among people, strong versus weak ties, and gender homophily.
5 Appendix: session
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3.2 Social capital is scarce and skewed
A firm of average position has about four interlocked partners. The upper tail stretches to 13. Nine firms have none. Betweenness is even more concentrated: many firms lie on almost no shortest path, and a few lie on a large share of them.
That shape is what a social-capital distribution should look like if the resource is an elite resource. Most organisations hold a little. A small inner set holds a lot. Isolates are the low-capital group in the strict sense: they have no access and no brokerage inside this set of firms.
The largest component contains 132 of the 143 firms. The remaining firms are nine isolates plus one small component. Mean distance inside the reachable pairs is 3.86 and the diameter is 9. The elite is not a complete clique. It is one loosely linked world with a centre.
Sub-conclusion: high social capital is a minority condition. Low social capital, including complete isolation from other firms in this sample, is common.