The small world of corporate boards

We demonstrate the importance of graph theory for understanding boards of directors. Specifically, we focus on the 'small world' phenomenon. Our empirical results show that a random graph model is remarkably good at explaining board structure and connectedness in the United States, the United Kingdom and Germany. Although there are small-world traits such as 'clustering' and 'short-paths' in the corporate world, they are no more pronounced than would be expected by chance in a statistically similar, but randomly assembled corporate universe. In short, boards of directors, especially in the United States, are no more 'clubby' than expected. Finally, our results show the existence of positive degree correlation: directors who sit on many boards do so in the company of other directors who sit on many boards. Board members whose services are in high demand, serve on boards with similar directors.