The Denseness of Social Networks

Researchers often study questions focused upon the individual. For example, how is a consumer influenced by an advertisement? What sort of skills are useful for a salesperson to possess? There are good reasons for this. Often we are seeking to give advice to individuals on how they should behave. Other times we are seeking to understand the decision making of individuals.

Clearly however this isn’t the full story of how the world works. Sometimes we are interested in the relationships between people which Social Network Analysis attempts to do. Each network, social group, can be expressed as nodes and edges. In a typical analysis the nodes will be people and the edges the connections between people, so friendships, working relationships, and family ties.

After mapping networks you may want to compare them. There are great visual ways of representing networks, I’ll discuss this in future posts, but visual networks are hard to compare. Ideally, we want measures of the network that are comparable across different networks. One such measure is the density of the complete network. This measures how highly the network members “are connected among themselves” (Knoke and Yang 2008, page 53).

Density represents the percentage of all the connections that could exist that actually do exist. So if everyone was connected to everyone else density would be one, if no one was connected to anyone else density would be zero.

Lets assume that we are examining an undirected network, so connections are mutual, if you know me I must also know you. To calculate density first count all the connections that exist in the network. Then find the number of connections that could exist. In small networks this can be done manually but the number gets very large, very quickly. We have a formula for the number of connections that exist when a number of people, denoted N, are linked, N!/(2!*N-2!). (! is factorial, use the command FACT() in Excel).

The level of density that you might expect depends upon the relationships that you are coding. If you count having met someone as a connection you will have a denser network that if you count only, relatively rare, academic co-authorships. Density represents an interesting way to start measuring the properties of social groups.

Read:David Knoke and Song Yang, (2008), Social Network Analysis, 2nd Edition, Sage Publications.