11 January, 2024

What is Metcalfe’s Law? Counting Communication Channels

By Mike Clayton


In this video, I want to answer the question, what is Metcalfe’s Law and how does it relate to the number of communication channels?

This video is safe for viewing in the workplace.

This is learning, so, sit back and enjoy

Metcalfe’s Law and Communication Channels

Communication Channels

When two people communicate with each other, they open a communication channel. As the number of people increases, so does the number of communication channels. But it increases far faster than the number of people. That’s the crux of Metcalfe’s Law.

  • When person A speaks with person B, there is one communication channel.
  • Now, when person C joins in, we have three people, and three communication channels.
  • And, when Person D arrives, we get four people… and 6 communication channels.
  • Then, five people and 10 channels
  • And then six people and 15 channels
  • 7 and 21
  • 8 and 28
  • 9 and 36
  • 10 and 45

And so on. At 20 people, we have 190 channels and at 50 people, we have 1,225.

The math of this is actually quite straightforward.

If you have n people, then each of them can connect with all the others – which is n-1 people. So, we can have n times n-1 connections. Except, we have double-counted. A connection from A to B is the same as the connection from B to A. So, we need to divide by two.

This gives us the number of connections as n times n-1, divided by two:

  • N = ½ x n x (n-1)

or, we can write:

  • N = n(n-1)/2

Metcalfe’s Law

This has the name, Metcalfe’s Law, after Robert Metcalfe. He first proposed this as a way to calculate the value of a telecommunications network, in 1980.

Notice that we can rewrite this as:

  • N = ½ x (n2 – n)

As the number of people gets very large, n2 becomes huge compared to n, and so we can approximate the formula to:

  • N ~ ½ n2

That’s actually Metcalfe’s Law – that the financial value of a telecommunications network is proportional to the square of the number of connected users of the system (n2).

The Significance of Metcalfe’s Law for Project Managers

As the number of people on our project grows, the complexity of managing them grows too. But much faster. Managing twice as many people all communicating with one another, is not twice as much work – it’s four times as much. Tripling the size of a project multiplies the communication challenge nine-fold.

This is why totally flat structures cannot work for large projects. We need to break them into workstreams and direct most communication between workstreams through the workstream leaders.

And as projects get huge, we aim to split them into multiple smaller projects, and coordinate them through the vehicle of a program.

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Mike Clayton

About the Author...

Dr Mike Clayton is one of the most successful and in-demand project management trainers in the UK. He is author of 14 best-selling books, including four about project management. He is also a prolific blogger and contributor to ProjectManager.com and Project, the journal of the Association for Project Management. Between 1990 and 2002, Mike was a successful project manager, leading large project teams and delivering complex projects. In 2016, Mike launched OnlinePMCourses.
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