This is a graph of Peertube instances following each other. There are 942 nodes and 10067 edges.

On Peertube, an instance X can follow an instance Y to let its users see all the videos posted on Y. This graph is a directed graph.

Color and size of nodes depends on how big their Eigenvector centrality is. Nodes which have 0 centrality are blue and small, nodes with bigger centrality are big and red.

What centrality represents? Instances which are not followed by anyone have 0 centrality. Instances (A) with a lot of followers (B) have bigger centrality. If those followers (B) themselves have followers (C), it means centrality of A will be even higher.

Does it mean anything in context of Peertube? I'm not sure. Considering chain of three instances: (A) <- (B) <- (C), when (A) posts a video, does it appear in (C)? Probably not. But if it was so, then centrality would've mean this: Videos posted on instances with high centrality spread across entire network, while videos posted on instances with 0 centrality are not visible anywhere else.

Here are top 10 instances and their centrality:

• http://tilvids.com/ 1.0
• http://share.tube/ 0.97
• http://conf.tube/ 0.90
• http://video.lqdn.fr/ 0.88
• http://skeptikon.fr/ 0.86
• http://spectra.video/ 0.74
• http://video.monsieurbidouille.fr/ 0.73
• http://aperi.tube/ 0.71
• http://tube.aquilenet.fr/ 0.71
• http://video.hardlimit.com/ 0.68

How to repeat this graph visualization

1. Download latest Peertube instances.csv and interactions.csv files here: https://www.kaggle.com/datasets/marcdamie/fediverse-graph-dataset-reduced
2. Import them to Gephi;
3. Apply Giant Component filter to remove nodes which are not connected to biggest network;
4. Apply ForceAtlas 2 layout;
5. Run Eigenvector centrality Statistics (directed). It will add a new column to nodes table;
6. Apply Nodes - Color - Ranking - Eigenvector centrality;
7. Apply Nodes - Size - Ranking - Eigenvector centrality;
8. Configure Preview and export.

P.S. On colorful image used as thumbnail of this post nodes are colored by Modularity (community detection).