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24 - Community Detection

from Part IV - Network Inference

Published online by Cambridge University Press:  11 June 2026

A. D. Barbour
Affiliation:
Universität Zürich
Gesine Reinert
Affiliation:
University of Oxford
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Summary

A number of methods for finding communities in networks are introduced, and their performance on two benchmark networks is compared. The chapter begins with methods of comparing classifications and for assessing the quality of a classification. Then, a number of classification algorithms that use modularity as a measure of quality are presented. An alternative approach is to fit a stochastic blockmodel to a network. Methods for doing so include a Bayesian approach based on the Gibbs sampler, and a variational method that makes use of the EM algorithm; estimation of the number of blocks is also considered. Spectral classification methods are described, including those based on the spectral decomposition of the non-backtracking matrix. The performance of the algorithms on two benchmark data sets is encouragingly consistent. The chapter concludes with two methods designed to find overlapping clusters, and with a discussion of the theoretical detectability threshold.

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