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Table 3 Summary of structural characteristics of the Instances network, including details on community structure and core decomposition

From: Understanding the growth of the Fediverse through the lens of Mastodon

  Instances Instances inner-most core
Degree In-degree Out-degree
#Nodes 6960 189 208 196
#Edges 216,504 25,790 28,690 26,463
Reciprocity 65.1% 88.4% 85.7% 88.2%
Density 0.004 0.726 0.666 0.692
Average degree* 41.966 152.328 157.702 150.98
Average in-degree 31.107 136.455 137.933 135.015
% Sources 12% 0% 0% 0%
% Sinks 6.6% 0% 0.005% 0%
Degree assortativity* − 0.274 − 0.117 − 0.158 − 0.135
Degree assortativity − 0.253 − 0.14 − 0.171 − 0.151
Average path length 2.330 1.270 1.330 1.310
Diameter 5 2 2 2
Transitivity* 0.128 0.832 0.798 0.807
Clustering coefficient* 0.836 0.837 0.810 0.816
Clustering coefficient (full averaging)* 0.687 0.837 0.810 0.816
#Strongly connected components 1305 1 2 1
#Weakly connected components* 1 1 1 1
Modularity by Louvain* 0.289 0.032 0.039 0.037
#Communities by Louvain* 5 (5) 3 (3) 3 (3) 3 (3)
Modularity by Louvain** 0.353 0.242 0.246 0.246
#Communities by Louvain** 6 (8) 4 (5) 3 (4) 4 (6)
#Communities by Infomap** 6 (54) 1 (3) 1 (4) 1 (3)
  1. *Statistic calculated by discarding the edge orientation
  2. **Statistic calculated by taking into account the edge weights