An MBO method for modularity optimisation based on total variation and signless total variation

In network science, one of the significant and challenging subjects is the detection of communities. Modularity [1] is a measure of community structure that compares connectivity in the network with the expected connectivity in a graph sampled from a random null model. Its optimisation is a common a...

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Bibliographic Details
Published inEuropean journal of applied mathematics pp. 1 - 83
Main Authors Li, Zijun, van Gennip, Yves, John, Volker
Format Journal Article
LanguageEnglish
Published Cambridge University Press 25.11.2024
Subjects
62H30
65K10
91C20
91D30
94C15
community detection
data clustering
Ginzburg–Landau functional
MBO scheme
modularity
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Summary:In network science, one of the significant and challenging subjects is the detection of communities. Modularity [1] is a measure of community structure that compares connectivity in the network with the expected connectivity in a graph sampled from a random null model. Its optimisation is a common approach to tackle the community detection problem. We present a new method for modularity maximisation, which is based on the observation that modularity can be expressed in terms of total variation on the graph and signless total variation on the null model. The resulting algorithm is of Merriman–Bence–Osher (MBO) type. Different from earlier methods of this type, the new method can easily accommodate different choices of the null model. Besides theoretical investigations of the method, we include in this paper numerical comparisons with other community detection methods, among which the MBO-type methods of Hu et al. [2] and Boyd et al. [3], and the Leiden algorithm [4].
ISSN:0956-7925
1469-4425
DOI:10.1017/S095679252400072X