The number of users by instance in #mastodon is highly unequal. Some servers (mastodon.social) have a significant fraction of the number of users. If the ubiquitous "rich-get-richer" (RGR) phenomenon kicks in, we might end up with a couple of instances having all of the users. But did it kick in? Here is the relationship between instance's size and growth. There is a little bit of RGR, but some of the rapidly-growing instances are small. Decentralization also in how the network grows.
You can see how unequal is the distribution of sizes by looking at the horizontal axis (note that it is in log-scale). Also @manlius has a recent toot about this: https://mathstodon.xyz/@manlius/109383027753990134
Manlio De Domenico (@[email protected])

Attached: 1 image Again, a quick and dirty analysis, but if I have no bugs then the 1% largest #Mastodon instances accounts for 84% of all users. The top 5% accounts for 97% of all users. We can say that the system is effectively centralizing around a few instances, and this might be a problem for the overall stability and sustainability. @[email protected] @[email protected] @[email protected] @[email protected] @[email protected] @[email protected] #MastoStat #ComplexSystems

Mathstodon
Thanks to @mauforonda for making the data of the growth on different instances available. Here is his fantastic visualization about these data https://observablehq.com/@mauforonda/what-goes-on-in-mastodon
What goes on in Mastodon

See values that don't make sense? Sometimes the source has trouble and stops updating for a while. This usually results in major instances like `mastodon.social` or `pawoo.net` dissapearing from the charts. Here's a plot to check how fresh the records in this page are. Other times instances will report wrong values. This usually shows as huge and sudden jumps in the user counts of clearly small or even personal instances. For example, since February 2023 many calckey instances that updated to recent builds

Observable