One of the key factors that drives whether a idea or brand flows through the social graph is the level of interconnectedness a specific social network has. How connected is my social network? Do all of my friends know each other? Do they share ideas and news? Watts and Strogatz came up with the idea of the clustering coefficient as a measure of how connected a social network was. It is calculated by dividing the number of links in the network by the maximum possible number of links.
The closer to 1 the coefficient is the more interconnected your network, and the smaller a world it is, making it easier for information to flow through its pathways. The maximum number of links can be calculated using the following formula n*(n-1)/2. Where n is the number of people in the network. The Friend Wheel application on facebook, can be used for illustrating how connected your facebook friends are.
In my network there are 30 people, meaning that there are 435 maximum links, and there are currently 82 links between them, giving me a coefficient of 0.189. This means my network is fairly interconnected, but most don't know each other. This isn't surprising when I think about it. Many are ex-colleagues, some family, and many are friends from different pockets of my past that I re-connected with through facebook. Within each pocket of clustered links they use similar applications. This demonstrates that interconnectedness drives idea flow through the graph. The challenge for brands going forward is going to be how to manage this flow so they are able to jump across the gaps that exist between connected networks. Or they could just help more people become better friends!