cross-posted from: https://mander.xyz/post/49566880

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

Eigenvector centrality

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 ©, 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) <- ©, when (A) posts a video, does it appear in ©? 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:

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.

Gephi

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

  • atro_city@fedia.io
    2·
    18 days ago

    I don’t understand the term “centrality”. It seems to actually be showing followship or reachability. Centrality sounds like more people use it instead of other instances or percentage of content that is from that instance alone. 100% centrality would thus mean the instance only has its own videos and doesn’t make other videos available, while 0% centrality means it only makes videos from other instances available.

    • podbrushkin@mander.xyzOP
      1·
      18 days ago

      I agree, “reachability” better explains this metric. But “centrality” is a well-defined term from graph theory. Also, center usually is easiest to reach from any given point (e.g. in cities). As for amount of active users, local videos or number of outgoing “follows” relationships for any instance - those metrics do not need a colorful picture and they nicely fit into this table: https://instances.joinpeertube.org/instances

      • atro_city@fedia.io
        1·
        18 days ago

        From that perspective, centrality makes sense 🤔 Maybe it’s just me but for this context, it seems very counter-intuitive. It may be right for graph theory, but when talking about the fediverse, not so much IMO.

        • podbrushkin@mander.xyzOP
          2·
          18 days ago

          for this context, it seems very counter-intuitive

          That’s very probable. Wait till I will get a graph where edges represent “blocks” relationships, will run same algorithm and will again say it’s centrality.