“Network density” as a measure of network health and effectiveness. I think network density has important ramifications for the way business works and for making the world a better place.

To better understand what it is, this article will show you how to easily calculate network density. The goal isn’t to get you calculating the network density of your Facebook connections – although you probably *could* if you wanted. No, the idea is to take just a few minutes to understand this easy calculation, as a way to give you a more intuitive feel for what network density is. With that, you’ll be better positioned to actually apply this important concept in your work.

## What is Network Density?

First a few quick definitions. In a network, the things that are connected are usually called *“nodes.”* A node might be a person, a computer, or even some hyperlinked text. The bridges between nodes are technically called *“edges,”* but for the purpose of this article I simply refer to them with the less technical term, “connections.”

“Network density” describes the portion of the *potential* connections in a network that are *actual* connections. A *“potential connection”* is a connection that could potentially exist between two “nodes” – regardless of whether or not it actually does. This person *could* know that person; this computer *could* connect to that one. Whether or not they *do* connect is irrelevant when you’re talking about a potential connection. By contrast, an *“actual connection”* is one that actually exists. This person *does* know that person; this computer *is* connected to that one.

A couple of examples might help. At a family reunion, the *actual* connections between people are quite numerous – it may even be a hundred percent of all the potential relationships in the room. In contrast, the *actual* connections between people on a public bus – the number of people who actually *know* each other – is likely to be quite low relative to all the *potential* relationships there.

A family reunion has high network density, but a public bus has low network density.

## Calculating Network Density:

So, here’s how you calculate network density. In the below chart, “PC” is “Potential Connection” and “n” is the number of nodes in the network. Don’t let the numbers turn you off; they’re actually pretty straightforward:

In the above chart, examples “A” and “B” illustrate cases where the number of *actual connections* between nodes is exactly the same as the number of *potential connections.* You can’t draw any new lines to connect these nodes; they’re all already connected. They’re perfectly “dense.”

Now take a look at example C. Like example B, there are three nodes. But in this case, two of the nodes (the top and bottom ones) aren’t connected to each other. This little network is missing one of its *potential connections*, and as a result, its network density drops to two-out-of-three, or 66.7%.

To scale things up with a bit larger example, let’s say a grocery store has a customer network with a hundred people in it. The total number of *potential* connections between these customers is 4,950 (“n” multiplied by “n-1” divided by two). So, if, of those *potential* connections, there are only 495 *actual* connections, the network density would be 10%. If the number of actual connections were 2,475, then the network density would be 50%.

There you go. Now you know how to calculate network density. Here’s some more good stuff about networks.

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MoonThank you for your explanation. It does really help me to understand the way to calculate the density. I just have a question about reading the number of density then. I actually used the KH coder to analyse textual data for word network and it says the value of density is .087. And I am not sure what it does mean. Does mean the nodes and edges have dense connections or not? What is the standard value of the density?

Moon

BSc undergraduate, University of Surrey

KwintijnNot really, the maximum value is 1. So 0.087 would be 8.7%, not really dense but still somewhat connected 🙂

lissyHow would this work if, for example I have a network that consists of 38 people and each person identifies up to 10 connections. Since the participants were not asked about more than 10 connections, can network density still be calculated?

Gideon RosenblattIt all depends on your definition of the network. In other words, you need a denominator, which is the total number of people in the network. If each of the 38 people had exactly 10 people and there were no overlap, that would create (380*379)/2, or 72,010 potential connections. And then you figure out how many of those actual connections and use that as the numerator. But the key point is that you need to have a clear definition of the network for this to work.

SAMSONHi, I have 10 nodes out of which 6 nodes have low connection and remaining 4 have medium connection. I have calculated the PC; 10*(9)/2=45. The network density of low connection is 6/45=0.133 (13%) and for medium connection is 4/45=0.88 (9%). Is this correct what I have done? Or should take the “n” value seperately for low and medium (i.e., n=6 and n=4)?

Gideon RosenblattYes, if you want to keep these two weightings separate. To assess overall density, you would have to figure out how to weight the value of low versus medium connection.

ThijsHi, thanks for the simple explanation! I’m writing my dissertation on whether sustainable start-ups require a denser network than convention start-ups. This is theorized because “green” start-ups face more unique challenges that stakeholders also need to understand and they incur more/different costs due to, for example, EMS systems. They might benefit from dense networks by sharing information and costs with key players.

I’m having difficulties, however, with an effective way to measure their potential network. The network of a start-up appears to be so immense, that I can’t think of a method to capture all potential nodes. I know that I have to split it up in multiple networks, but do you maybe have some suggestions on what I should not forget to include when I start collecting data? All start-ups are geologically bound to a city (Amsterdam and Eindhoven). So I know I could look at ties with Universities, Venture capital, governments, etc… But HOW do I analyse the potential nodes with those networks. I know this is a lot to ask, but any tip regarding data collection would help me out!:) kind regards.

Gideon RosenblattIt’s a really interesting question. Trying to map out stakeholders is tricky work. I’m heading into a Zoom call right now, but try looking at snowball sampling. That might be a path for you:

https://en.m.wikipedia.org/wiki/Snowball_sampling

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ahi, can we use network density as an independent variable while performing ordinary linear squares regression?

MoseWhile calculating network density, can we include singletons connections?

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Gail James RomaWell explained; great example.

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