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Explicit objective functions in modularity-based community detection on multiplex networks — arXiv:2609.37253

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.37253
License (as archived): CC0-1.0
Archived: 2026-10-07T17:26:29.491Z
SHA-256 of the archived text: 8d7ec1f97ce67093ebde0e26164cd50f566d75d6505a7b90b229dab4c30999cd
Stable URL of this page: https://metraipolis.com/documento/dc_83bf59f855fd

How to cite

Explicit objective functions in modularity-based community detection on multiplex networks — arXiv:2609.37253 — arXiv (en), https://arxiv.org/abs/2609.37253 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_83bf59f855fd (Metraipolis archive dc_83bf59f855fd, sha256 8d7ec1f97ce67093ebde0e26164cd50f566d75d6505a7b90b229dab4c30999cd)

BibTeX

@misc{dc83bf59f855fd,
  title = {Explicit objective functions in modularity-based community detection on multiplex networks — arXiv:2609.37253},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.37253},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_83bf59f855fd; sha256 8d7ec1f97ce67093ebde0e26164cd50f566d75d6505a7b90b229dab4c30999cd},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.37253. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Modularity-based community detection in multiplex networks is commonly approached through one of three strategies: early fusion (EF), which first aggregates the layers into a single network and then applies community detection; simultaneous fusion (SF), which combines information from the layers during modularity optimization; and late fusion (LF), which combines the community assignments obtained by detecting communities separately in each layer. Although recent taxonomies and surveys distinguish these strategies conceptually, their objective functions have rarely been compared analytically. We provide such a comparison for shared-node multiplex networks with normalized non-negative edge and layer weights, a common resolution parameter, and no interlayer edges. Node-attributed networks are represented by topology and attribute-similarity layers. We use a common notation for the three formulations and derive explicit relationships between their objective functions. In particular, we show that the EF objective equals the SF objective plus a non-negative heterogeneity term. We prove that the SF objective admits an optimal layer-weight vector at a simplex vertex, although nonvertex optima may also occur under ties, whereas the EF objective is concave with respect to the layer parameter for each fixed partition, and its joint optimum may occur in the interior of the simplex. For LF methods, the resulting objective and conclusions depend heavily on how the transient graph is constructed. In this study, we focus only on one of such LF methods. We complement the analytical results with brute-force experiments on synthetic multiplexes and heuristic experiments on real-world networks, including node-attributed networks represented as multiplexes. The experiments illustrate the analytical results and the influence of heuristic optimizers on the observed comparisons.

Tema degli esploratori: governance digitale e beni comuni (retro-catalogo arXiv: annunci del 2026-09-30 in cs.SI).
Categorie arXiv: Social and Information Networks (cs.SI).
Pagina del lavoro: https://arxiv.org/abs/2609.37253 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T16:58:01.668Z dalla pagina https://arxiv.org/catchup/cs.SI/2026-09-30?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).