These remarks highlight the fact that the properties of a social network can never be inferred simply from the mathematical measures that it is possible to make. It is always necessary to ensure that the measure can be given a substantive sociological significance.
The degree of a point—its total of incoming and outgoing lines—is the most basic measure and has been termed local centrality.
distance-based measure of ‘closeness’ has generally been preferred as a measure of global centrality.
The density of a graph is a very useful and direct measure of its cohesion, but it has one major limitation as a comparative measure of social structure. In real situations, density varies with the size of a network and this limits the possibilities of using the measure to compare different types of network. It is highly unlikely that agents are able to sustain more than a certain number of relationships: our ability to be ‘friends’ with people, for example, has its limits. Other things being equal, then, an increase in the size of a network is likely to mean a reduction in its density.