Community Detection in Multilayer Networks

Community detection seeks to partition a network’s nodes into modules or clusters that are more densely connected internally than with the rest of the network. In multilayer networks, nodes may interact through several types of relationships or across time, giving rise to layers that capture distinct modes of connectivity. Identifying communities within and across layers reveals hidden organisation in social systems, biological pathways, transportation infrastructures and financial markets. Unlike single-layer approaches, multilayer methods must account for interlayer coupling, variable layer significance and potential overlaps between communities. Recent advances include probabilistic generative models that infer latent block structure, flow-based techniques that compress dynamics across layers, optimisation frameworks that generalise modularity to account for layer dependencies, and matrix-factorisation methods that jointly decompose adjacency information. Challenges remain in balancing computational scalability with accuracy, handling heterogeneous layer topologies, and detecting both persistent and transient communities. Practical applications range from mapping cellular modules across omics layers to tracking evolving social groups and designing resilient interdependent infrastructures.

Research from Nature Portfolio

SimMod introduced a mathematical-programming approach to detect composite communities in multiplex biological networks by integrating physical, genetic and co-expression interactions into a single representative partition. This method demonstrated enhanced functional enrichment compared with aggregated or single-layer partitions, without requiring prior training on known interactions. In a separate study, a null-model framework for multiplex networks relied on node redundancy to define modularity and uncover community structure across multiple relationship types. Application to empirical multiplex datasets revealed communities that standard null models or aggregated analyses would obscure, providing deeper insight into the specificity of multilayer connectivity patterns.

Research from all publishers

An orthogonal nonnegative matrix tri-factorisation method was proposed to identify both common and layer-specific communities in multiplex networks. By representing each layer’s adjacency matrix as the sum of low-rank factors for shared and private modules, the approach determines the number of communities automatically and demonstrates robust performance on synthetic and real datasets. A hierarchical stochastic block model for multiplex networks employed Bayesian inference to uncover nested community structure across layers. This framework models both shared and layer-unique partitions, utilises hierarchical priors to capture multiscale organisation, and provides statistically grounded estimates of model complexity, outperforming flat block models in recovering planted communities.

Community Detection in Multilayer Networks publication trend

The graph below shows the total number of articles in community detection in multilayer networks across all publications each year (not limited to Nature Index journals).

Technical terms

Multilayer network: A graph model in which nodes are connected by edges in multiple layers, each representing a distinct type or time of interaction.

Community structure: The organisation of nodes into groups with dense intra-group connections and sparse inter-group ties.

Modularity: An objective function that quantifies the quality of a network partition by comparing observed intra-community edges to those expected under a null model.

Stochastic block model (SBM): A generative model that assigns nodes to blocks and places edges probabilistically based on block memberships.

Nonnegative matrix factorisation: A method that decomposes a nonnegative matrix (such as adjacency data) into factors whose entries are constrained to be nonnegative, often used for latent community detection.

References

1. Detection of Composite Communities in Multiplex Biological Networks. Scientific Reports (2015).
2. Null Model and Community Structure in Multiplex Networks. Scientific Reports (2018).
3. Community Detection in Multiplex Networks Based on Orthogonal Nonnegative Matrix Tri-Factorization. IEEE Access (2024).
4. Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks. Bayesian Analysis (2024).