Community structure and centrality effects in the South African company network

This paper conducts a search for community structure in the South African company network, a social network whose elements are South African companies listed on the Johannesburg Stock Exchange. Companies are connected in this network if they share one or more directors on their respective boards. Discovered clusters, called communities, can be considered to be compartments of the network working relatively independently of one another, making their distribution and composition of some interest. We test whether the discovered communities of companies are (a) statistically significant, and (b) related to other attributes such as sector membership or market capitalization. We also investigate the relationship between the centrality of a company's position in the network and its market capitalization.