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Community validation #
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See also Cluster validation for general clustering validation.

Given ground truth, Mutual information is often used. An important, overlooked question is how good the ground truth is. Some work about tagged networks^1[^3].

Statistical significance of communities: http://www.pnas.org/content/108/18/7321.short ; http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0018961

Overlapping community structure makes the problem harder. For instance, Mutual information should be extended to covers. There are two proposals[^4][^5]. There are other suggestions: using conductance of boundary nodes[^6].

An approach to use data[^7].

References #

How can we define statistical significance? What will be the proper null models for community structure?

There are approaches to use online social network services such as Facebook (http://fellows-exp.com/).

^1: Palla, Gergely; Farkas, Illés J; Pollner, Péter; Derényi, Imre; Vicsek, Tamás (2008). "Fundamental statistical features and self-similar properties of tagged networks". New Journal of Physics 10 (12): 123026. doi:10.1088/1367-2630/10/12/123026. ISSN 1367-2630

^2: Pollner, Péter; Palla, Gergely; Vicsek, Tamás (2010). "Clustering of tag-induced subgraphs in complex networks". Physica A: Statistical Mechanics and its Applications 389 (24): 5887–5894. doi:10.1016/j.physa.2010.09.012. ISSN 03784371.

[^3]: Tibély, Gergely; Pollner, Péter; Vicsek, Tamás; Palla, Gergely (2012). "Ontologies and tag-statistics". New Journal of Physics 14 (5): 053009. doi:10.1088/1367-2630/14/5/053009. ISSN 1367-2630.

[^4]: Lancichinetti, Andrea; Fortunato, Santo; Kertész, János (2009). "Detecting the overlapping and hierarchical community structure in complex networks". New Journal of Physics 11 (3): 033015. doi:10.1088/1367-2630/11/3/033015. ISSN 1367-2630.

[^5]: "Template:Citation error". http://arxiv.org/abs/1202.0425.

[^6]: "Evaluating Overlapping Communities with the Conductance of their Boundary Nodes". http://arxiv.org/abs/1206.3992.

[^7]: "Benchmarking community detection methods on social media data". http://arxiv.org/abs/1302.0739.

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