Your Social Network Is Bigger Than You Think!

Your social network is bigger than you think!

I remember what got me really interested in social network analysis as a field of academic study was just the scale at which these networks grow.

Whether we are looking at how people talk with others or share things with other people, these interactions can grow to massive sizes in examined in full detail.

This due to what is known as the “Six degrees of separation” whereby you are never more than six degree (six people) away from every one else in the network. I’m sure you’ve heard of the six degrees of Kevin Bacon, but the general rule applies.

Your social network has potential, and I can prove this using basic some basic graph theory and data science techniques.

What with Mastodon, surpassing 10M users recently, I decided to put this to the test and see the results for myself using my own Mastodon followers.


The general idea is simple. The algorithm goes something like this:

  1. Get a list of people who follow me on Mastodon
  2. Add them to queue
  3. For each account in the queue, get their followers and add them to the queue (if not already in the queue)
  4. Repeat

At each interaction, all the followers are added to a directed graph such that an edge represents “A follows B”.

Due to the exponential growth of the network, each iteration will be much larger than the previous. This is a recursive process which will eventually crawl the entire Mastodon network.

This would result in a massive network which, even my beefy MacBook Pro, couldn’t handle, but let’s see how far we can take this.

My plan is to repeat this for as many interactions as possible, but this might involve setting a cut-off point at, say, 3 or 4 iterations depending on the size of the network.

But anyway, let’s see how far we can get!

First Iteration

And so on the first pass, we are just focusing on my immediate followers. I don’t exactly have a ton of followers at the moment (33, in fact, as of this writing). You can find me at @jrashf if you want to boost these numbers.

At the moment, we have what is known as an ego network where all connections are centred around a single node.

Here is what the resulting network looks like when visualised, where the big red node represents the user of interest, in my case, me.

Second Iteration

After the second pass, (two hops way from me) this is where the numbers start to get bigger.

We now have a total of 6,753 users (again, not include me) which is an increase of 6,720 (20363.6%).

That is a massive increase!

Again, here is what the results look like when visualised. The red node (me) acts as the “You Are Here” in the follower network.

Comparing this to the previous network, you can start to see how the community starts to take formation as some of my followers have mutual connections. This is beginning to revel the small-world dynamics of follower networks.

Scale Estimates

Unfortunately, this is as far was I can get without hammering the Mastodon API (which I don’t really want to do as I don’t want to get into any trouble) and without encountering any rate limiting issues.

I decided to stop things from here, as things were starting to get too big for me to handle.

But, with this in mind, let’s make some hypothetical estimates…

Of my immediate followers, each one of them has, on average, 199 followers. Assuming that this pattern is consistent (which, of course, it isn’t) this means that the next layer of followers could include a total of 6,720 X 199 = 1,337,280 new users.


Let’s visualise these figures to see how they compare to the previous networks. The estimated value for the third pass were so high I had to set the y-axis to a logarithmic scale.

As, I’m sure you can imagine, these numbers will only get bigger for the fourth, fifth, and eventually, sixth iteration.

Final Thoughts

Hopefully, I’ve proved my point that social networks are a fundamental component in order for information to reach others at scale. Just imagine what this would look like for someone with a really large following!

This is essentially the basis for how content goes viral on social media in fact, information like this can spread in a way similar to that of an epidemic (let’s not talk too much about epidemics, as we all know too well what they are like based upon events in recent years).