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Table 2 NMI of the metadata communities and the communities detected by several algorithms applied to five network datasets: Zachary Karate Club (Zachary 1977), 2000 US College football (Girvan and Newman 2002), the 2004 US Political Books from Amazon (Krebs 2008), the US Political Blogs (Adamic and Glance 2005), and a small portion of the Facebook social network (Traud et al. 2012). For Facebook we consider different metadata to define communities. The first four columns report respectively name of the network (and eventual metadata used to define communities), number of nodes N in the network, number of edges M, and number of communities C according to the metadata classification. All other columns refer to results obtained using community detection algorithms. First, we considered our proposed algorithms (original and reduced) and the two different starting conditions (random and regular). Given the stochasticity of the outcome, we report median values and the 90% confidence interval for NMI values. Due to its high computational complexity, we couldn’t use the original version of the our proposed algorithm to analyze large networks. We performed the same analysis using Louvain and Infomap. In this case, the outcome of the community detection algorithm is deterministic, so we report a single NMI value

From: Error-correcting decoders for communities in networks

     Original random Original regular Reduced random Reduced regular Louvain Infomap
Graphs N M C 5% 50% 95% 5% 50% 95% 5% 50% 95% 5% 50% 95% 50% 50%
Karate 34 78 2 0.23 0.43 0.49 0.38 0.47 0.51 0.21 0.68 0.84 0.00 0.00 0.84 0.52 0.58
Football 115 615 13 0.72 0.78 0.81 0.86 0.89 0.90 0.86 0.94 0.98 0.34 0.83 0.98 0.21 0.49
Polbooks 105 441 3 0.42 0.45 0.48 0.43 0.45 0.47 0.27 0.62 0.66 0.60 0.62 0.70 0.04 0.11
Polblogs 1222 16714 2 - - - - -   0.53 0.59 0.67 0.04 0.78 0.79 0.01 0.02
fb-dorm 10001 362892 112 - - - - - - 0.01 0.11 0.12 0.01 0.06 0.13 0.21 0.13
fb-gender 10001 362892 7 - - - - - - 0.00 0.01 0.03 0.01 0.01 0.02 0.00 0.01
fb-high school 10001 362892 691 - - - - - - 0.13 0.16 0.17 0.02 0.08 0.16 0.10 0.29
fb-major 10001 362892 180 - - - - - - 0.01 0.08 0.09 0.01 0.06 0.07 0.03 0.12