A note on network structure: functional relationships between network indicators

Two important aspects of network structure are network density and network centrality. These two aspects highlight different characteristics of a network. Empirical studies tend to find that one or the other is the better explanatory variable for certain aspects of corporate behaviour. This note makes a simple and compelling point. There is a hill-shaped relationship between network density and network centrality. A purely stochastic process of alliance formation will lead to a hill-shaped relationship. A mathematical, functional relationship can be shown between network density and the upper bound to network centrality. The combination of these outcomes sets lower and upper bounds on network centrality. This approach can offer a vantage point for an evolutionary study of network structure.