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Networks offer a compact representation of complex systems such as social, communication, and biological systems. Traditional network models are often inadequate to capture the diverse nature of contemporary networks, which may exhibit temporal variation and multiple types of interactions between entities. Multilayer networks (MLNs) provide a more comprehensive representation by allowing interactions between nodes to be represented by different types of links, each reflecting a distinct type of interaction. Community detection reveals meaningful structure and provides a better understanding of the overall functioning of networks. Current approaches to multilayer community detection are either limited to community detection over the aggregated network or are extensions of single-layer community detection methods with simplifying assumptions such as a common community structure across layers. Moreover, most of the existing methods are limited to multiplex networks with no inter-layer edges. In this paper, we introduce a spectral-clustering-based community detection method for two-layer MLNs. The problem of detecting the community structure is formulated as an optimization problem where the normalized cut for each layer is minimized simultaneously with the normalized cut for the bipartite network along with regularization terms that ensure the consistency of the within- and across-layer community structures. The proposed method is evaluated on both synthetic and real networks and compared to state-of-the-art methods. MLNs. The problem of detecting the community structure is formulated as an optimization problem where the normalized cut for each layer is minimized simultaneously with the normalized cut for the bipartite network along with regularization terms that ensure the consistency of the intra- and inter-layer community structures. The proposed method is evaluated on both synthetic and real networks and compared to state-of-the-art methods.
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This content will become publicly available on December 1, 2026
Multiplexity amplifies geometry in networks
Many real-world networks are multilayer, with nontrivial correlations across layers. Here, we show that these correlations amplify geometry in networks. We focus on mutual clustering—a measure of the number of triangles that are present in all layers among the same triplets of nodes—and find that this clustering is abnormally high in many real-world networks, even when clustering in each individual layer is weak. We explain this unexpected phenomenon using a simple multiplex network model with latent geometry: Links that are most congruent with this geometry are the ones that persist across layers, amplifying the cross-layer triangle overlap. This result reveals a different dimension in which multilayer networks are radically distinct from their constituent layers.
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- Award ID(s):
- 2311160
- PAR ID:
- 10653501
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Research
- Volume:
- 7
- Issue:
- 4
- ISSN:
- 2643-1564
- Page Range / eLocation ID:
- L042046
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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