Multilayer Closeness Centrality
Multilayer Closeness Centrality (Generalized Closeness for Multilayer Networks) · Also known as: multilayer closeness, multi-layer closeness centrality, MLC, interlayer closeness centrality
Multilayer closeness centrality extends the classical closeness centrality measure to networks that contain multiple types of relationships or interaction contexts (layers). Rather than treating each layer in isolation, it computes how quickly a node can reach all others by traversing any combination of available layers, revealing nodes that are structurally efficient connectors across the full network system.
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When to use it
Use multilayer closeness centrality when your data contain multiple, simultaneously active relationship types (e.g., social media platforms, transportation networks with rail and road, organisational ties by role) and you want to identify nodes that are globally efficient communicators across all layers combined. It is especially valuable when information or resources can flow via any available channel. Do not use it when layers are truly independent processes with no meaningful path between them, when data are too sparse to yield reliable shortest paths, or when a simpler single-layer analysis adequately captures the phenomenon of interest.
Strengths & limitations
- Captures cross-layer reachability that single-layer closeness inherently misses.
- Identifies bridging nodes whose importance emerges only from combining multiple relationship types.
- Compatible with both weighted and unweighted multilayer structures.
- Provides a single comparable score per node despite multi-relational complexity.
- Useful for epidemiological, organisational, and transportation network analyses.
- Computationally expensive for large multilayer networks due to all-pairs shortest-path requirements.
- Results are sensitive to the choice of interlayer coupling weight, which is often not empirically grounded.
- Disconnected multilayer graphs require normalisation adjustments or restricted scope, complicating interpretation.
- Less intuitive to explain to audiences unfamiliar with multilayer network concepts.
Frequently asked
How does multilayer closeness differ from averaging closeness across layers?
Averaging single-layer closeness ignores cross-layer paths entirely. Multilayer closeness computes paths that can freely traverse any layer, so a node that links otherwise disconnected communities across layers receives a much higher score than averaging would suggest.
What is the supra-adjacency matrix?
The supra-adjacency matrix stacks all layer adjacency matrices and adds interlayer coupling blocks connecting the same node's copies across layers. Shortest paths computed on this expanded graph correspond to genuine multilayer traversal.
How sensitive are results to the interlayer coupling weight?
Very sensitive. A high coupling weight makes layer-switching cheap, reducing multilayer closeness to something close to the best single-layer closeness. A low weight discourages cross-layer hops. Always run a sensitivity analysis varying the coupling parameter.
Can multilayer closeness be computed for directed networks?
Yes. For directed multilayer networks, in-closeness and out-closeness are distinguished by whether shortest paths are computed from or to a given node. The supra-adjacency matrix is asymmetric in that case.
What software supports multilayer closeness centrality?
The Python library MuxViz and the R package multinet implement multilayer centrality measures including multilayer closeness. NetworkX can be adapted by constructing the supra-adjacency matrix manually.
Sources
- Kivela, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014). Multilayer networks. Journal of Complex Networks, 2(3), 203–271. DOI: 10.1093/comnet/cnu016 ↗
- Sole-Ribalta, A., De Domenico, M., Kouvaris, N. E., Diaz-Guilera, A., Gomez, S., & Arenas, A. (2013). Spectral properties of the Laplacian of multiplex networks. Physical Review E, 88(3), 032807. DOI: 10.1103/PhysRevE.88.032807 ↗
How to cite this page
ScholarGate. (2026, June 3). Multilayer Closeness Centrality (Generalized Closeness for Multilayer Networks). ScholarGate. https://scholargate.app/en/network-analysis/multilayer-closeness-centrality
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Closeness CentralityNetwork analysis↔ compare
- Multilayer Betweenness CentralityNetwork analysis↔ compare
- Multilayer Community DetectionNetwork analysis↔ compare
- Multilayer Degree CentralityNetwork analysis↔ compare
- Multiplex Network AnalysisNetwork analysis↔ compare