TABLE 5
FROM:
Comparing small world statistics over time and across countries: an introduction to the special issue comparative and transnational corporate networks
Bruce Kogut and Mariano Belinky
BACK TO ARTICLETable 5. Interlocking, 1990
| Country | Average path length | Clustering coefficient | ||||||
|---|---|---|---|---|---|---|---|---|
| Actual | Random | Robins randomization | Newman–Strogatz–Watts estimates | Actual | Random | Robins randomization | Newman–Strogatz–Watts estimates | |
| Germany | 2.6 | 2.1 | 2.7 | 2.1 | 0.39 | 0.049 | 0.11 | 0.10 |
| Sweden | 3.0 | 2.4 | 3.0 | 2.6 | 0.42 | 0.043 | 0.20 | 0.24 |
| Denmark | 2.5 | 1.5 | 4.1 | 2.5 | 0.73 | 0.152 | 0.19 | 0.63 |
| Norway | 4.2 | 3.8 | 3.9 | 3.0 | 0.48 | 0.053 | 0.20 | 0.23 |
| Switzerland | 2.6 | 2.2 | 2.7 | 2.3 | 0.41 | 0.09 | 0.20 | 0.15 |
| The Netherlands | 4.0 | 3.5 | 6.2 | 3.3 | 0.56 | 0.007 | 0.27 | 0.38 |
These tables summarize the results of calculating the inputs into the small world statistics for the board interlock network for the first country panels. To calculate the SW statistic, we need to have the empirical values (defined for average path length and clustering statistic in the description to Table 1) plus normalizing values as proposed by Watts and Strogatz (1998). This normalizing statistic serves the role of creating a standardized value that is no longer sensitive to the size of the network. Thus, we are able to compare networks of different sizes. The table offers three normalizing statistics. The first is simply the Erdos–Renyi value calculated by a formula given in the Watts and Strogatz text; it assumes a Bernoulli process that results in a Poisson degree distribution; technically, it is not appropriate for a bipartite network. The Robins randomization is found by taking the empirical network, choosing a link randomly, and then reassigning it to two other nodes randomly chosen; thus the density of the network is maintained. A constraint that the degree should not be less than two is standard in the literature, but nevertheless consequential as discussed in the text. The Newman–Strogatz–Watts estimates are derived using formulas that are derived from an application of generating functions that use the empirical bipartite degree distributions without specifying a specific distribution. The results show considerable variation among the approaches, which are best described by Tables 9, 10, 11 and 12 and Figures 1, 2 and 3.
