The development of structure in random networks: an analysis of the effects of increasing network density on five measures of structure

The density of ingroup relations continues to be proposed as an indicator of structural cohesion. Network density is obviously a misleading indicator of structural cohesion when a group has subgroups; in such circumstances, the cohesion may be entirely internal to the subgroups. However, it is plausible that network density is a useful indicator of structural cohesion when it can be assumed that a group lacks subgroups. In order to analyze this possibility, I construct a set of random networks, increase the density of relations in these networks, and observe how the networks' structure develops in terms of five measures. The results show that low densities in large networks may be associated with more structural cohesion than higher densities in smaller networks; it is suggested that in field studies, attempts to control for network size will encounter problems of nonlinearity and heteroscedasticity. I conclude that network density is not a useful indicator of structure and that direct measurement of structure is to be preferred.