What is Metcalfe’s Law? Counting Communication Channels

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?

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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.

Recommended Videos to Help with Metcalfe’s Law, Communication, and Project Management Math

Carefully curated video recommendations for you:

• Communications Channels: How to De-risk Your Project | Video
• Project Communication: Stop Using Telegrams – Get Better Project Results | Video
• How to Build a Great Project Communications Plan | Video
• Challenging Communication Tips for Better Project Communication | Video

Recommended Articles to Help with Metcalfe’s Law, Communication, and Project Management Math

• Project Management Formulas: How to Get a Grip on the Math of PM
• How to Get Project Communications Management Right… Every Time
• How to Create a Discounted Cash Flow – DCF Made Easy
• Earned Value Primer: The Basics of EVM

What Kit does a Project Manager Need?

I asked Project Managers in a couple of forums what material things you need to have, to do your job as a Project Manager. They responded magnificently. I compiled their answers into a Kit list. I added my own. 

Check out the Kit a Project Manager needs

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