A client and I are in the middle of a discussion about total second-level reach. The question is: how many total followers do my followers have? The answer is far less straight-forward than most analysts/agencies would have you believe.
A naive approach to this question would be to look at each follower and count the number of followers those users have. The problem with that approach is we double/triple/etc. count any individuals that are jointly followed by two/three/etc. of the followers. Many analysts will ignore this as being insignificant and just report the big number. Much easier. And completely wrong.
GraphEdge is less concerned with who is following a set of followers, and more concerned with who else the followers follow. That is, we look at the other people your followers follow, rather than who is following your followers (I know, it gets complicated!). However, from what we do calculate, I can tell you that it is not sufficient to take a total of followers’ followers and report that as second-level reach.
The reason is that it ignores “centrality” (for you academics). Imagine that me and ten of my friends are all following each other. My ten followers will each be following ten people. Add that up, and that’s 100 “connections”. But we know there are really only 10 unique individuals in that extended network (not counting me). That’s a 10% uniques-to-connections ratio.
Centrality tends to increase as the size of the network increases. So growing your network has marginally reduced effect on the size of the extended network.
To demonstrate this effect I took a random sample of 700 or so active GraphEdge accounts and looked at the number of followers, the number of connections to followers’ friends, and the number of unique names the followers were following. Note: for accounts with more than 10,000 followers, we generally take a sample of the followers, rather than looking at each follower’s network, so to keep the numbers clean I limited my sample of 700 accounts to those who had less than 10,000 followers.
This chart shows the total connections (blue dots), given a number of followers (on the X axis), and the number of unique individuals (red dots) in the set of followers’ friends. Notice how the number of unique individuals grows at a much slower rate than total connections, as the number of followers increases.
For example, let’s look at that first pairing at around 9K followers. The blue dot (the highest in the chart) says that those 9,000 or so followers had a total number of connections around 8M (close to 900 “friends” per follower). However, from the red dot directly below it, we can see that there were only 2M unique people in that list of 8M connections (more like 250 unique names per follower).
And this next chart breaks it down by the ratio of uniques-to-connections, given the number of followers.
Our friend with the 9,000 followers had a unique-names count just 25% or so of the total number of connections.
So if someone asks for a summed-total of Twitter followers’ followers: go ahead and present the number, but know (better yet, explain) that the real reach may well be just 30% of the number reported… or less! And if you need to calculate either one of them, let me know, I can help you there!