It is pretty clear to most that the number of connections in a network grows more quickly than the number of people in the network. It is a mathematically consistent relationship captured by Metcalf’s Law, but in summary, you double the size of a network, you quadruple the number of potential connections.
This relationship between the nodes in a network, and the number of (potential) connections is the foundation of social media, as the increase of the potential connections comes at little or no cost.
This is in complete contrast to the past, where these added connections added cost at a consistent rate, each new potential connection required someone to spend the time to make the phone call, mail the brochure, meet, discover if there was a potential value in devoting the resources to nurturing the relationship. All this cost prevented the development of the relationships that creates a network.
The relationship maths is the same, but the transactions costs associated with the “old economy” ensured that many things that now can happen, simply could not because of the costs involved. Hugely successful sites like Flikr simply could not have evolved with the transaction costs of the past involved.
The new challenge is harnessing the potential energy in these connections, and leveraging it to benefit the individuals in these potential networks enabled by the removal of the transaction costs.