A look at the law and numbers, Metcalf, Reed, Dunbar, and others

In order to understand the value and power of networks, such as a community, a number of individuals have come up with equations and analysis. It’s worth a bit of time to understand what they are talking about and how it may be useful to a CM.

Metcalf’s Law: Holds that the number of connections in a group grows very quickly as the number of members in the group increases. A group of two can have one connection, 3 members has 3, but 4 members has 6, 5 has 10, and so on.

For a CM, this shows how quickly opportunities for relationships increase as the group size gets bigger.

Reed’s Law: Reed adds the idea of a sub-group, or connections to a set of multiple people. Thus, a member may have a connection with a sub-groups made up of 2, 3, 4, 5, or more members. When this notion is taken up with Metcalf’s the number of possible connections grows exponentially. A group of two can have one connection, 3 members has 4, 4 members has 11, 5 has 26, and so on.

For a CM this means a member of a large group with subgroup ability has the benefit of many more possible connections than a member without subgroup ability.

A community that allows subgroups increases their possible interconnectedness exponentially.

It also means that a small increase in group size may quickly overwhelm anyone trying to keep a handle on various connections.

Dunbar’s Number: Is the number of individuals a person can maintain a relationship with. So, although Reed’s Law shows how quickly a person’s possible connections grow in a group, there may be a limit as to the number of connections a person can actually maintain.

Around 150 people is what Dunbar estimates a person may be able to maintain at any one time. This would include both online and offline. While others have come up with higher numbers, for a CM it means there is a limit.

Since there is a limit, it is best to put effort into making those connections of the highest value.

At only 8 members, Reed’s law put it at 242 possible connections. That may help explain the number of subgroups that don’t gain traction. Even with very few members, it is possible to have more connections than people can work with.

Perfect group size: Others have tackled this problem from a different angles and while there is no definitive number, or law, one could go with the number 6 as a rule of thumb. Part of this depends on the task and individuals.

When looking at creating subgroups, especially ones oriented toward tasks, it may be that these sort of smaller numbers are better.

How these laws and numbers work within your communities context will probably differ. This is even more true when you look at how active your members are, or not. My big take-away was just how quickly the opportunities for connections scale up, and can quickly overwhelm what an individual can use.

Much of this was taken from my exploration in and around Reed’s Law in Wikipedia.

About John

Interested in how information intersects daily life, technology, and art.
Collaboration specialist, working in social and collaborative media. Biomedical Informaticist, focusing on patient/patient, patient/provider communication.