Multilayer Betweenness Centrality
Multilayer Betweenness Centrality (Tensor-based Network Centrality) · Also known as: MBC, multilayer geodesic betweenness, tensorial betweenness centrality, interlayer betweenness centrality
Multilayer betweenness centrality extends the classical betweenness measure to networks with multiple types of relationships — or layers — by computing how often a node lies on shortest paths that can traverse any layer or switch between layers. It identifies brokers and bridges whose influence spans distinct interaction domains simultaneously.
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When to use it
Use multilayer betweenness centrality when your network data captures multiple distinct relationship types or contexts (e.g., online + offline ties, transport + social connections, co-authorship + citation) and you need to identify nodes that broker information or resources across layers — not just within a single layer. It is appropriate when inter-layer paths are meaningful and when cross-layer brokerage is a substantive research question. Do not use it when only one relationship type is present (plain betweenness centrality suffices), when inter-layer transition costs are unknown or arbitrary, when network layers are poorly defined, or when the network is so sparse that most node pairs have no connecting path.
Strengths & limitations
- Identifies brokers whose importance only becomes visible when multiple relationship types are considered together.
- Grounded in a rigorous tensor-based mathematical framework that generalizes classical betweenness to arbitrary layer structures.
- Applicable to both multiplex networks (same nodes, different edge types) and interconnected networks (different node sets per layer).
- Provides layer-resolved scores that reveal in which layers a node's brokerage is most active.
- Robust to layer redundancy: if two layers are nearly identical, the measure will not artificially inflate centrality scores.
- Computationally expensive: shortest-path enumeration in multilayer graphs scales poorly with the number of nodes and layers.
- Requires explicit specification of inter-layer coupling costs; results can be sensitive to these assumptions.
- Interpretation becomes complex when many layers are present, making it hard to explain which specific cross-layer paths drive high scores.
- Node alignment across layers must be established beforehand; mismatched or partially overlapping node sets complicate the analysis.
Frequently asked
How does multilayer betweenness differ from running betweenness separately on each layer?
Single-layer betweenness ignores paths that cross between layers. Multilayer betweenness finds the globally shortest paths over the entire coupled structure, so a node can score highly by bridging layers even if it is not particularly central within any single layer.
How should I set the inter-layer coupling strength?
Coupling strength should reflect the real cost or ease of switching between layers. If empirical data on switching costs are unavailable, it is advisable to run a sensitivity analysis across a range of values and report how rankings change.
Is multilayer betweenness centrality available in standard network libraries?
Yes. The MuxViz platform by De Domenico and colleagues is specifically designed for multilayer network analysis and includes multilayer centrality measures. Python-igraph and custom NetworkX extensions also support it.
When is the node-layer formulation preferable to the aggregate node formulation?
Use node-layer formulation when you need to understand in which layer a node's brokerage is active. Use the aggregate node formulation when the research question concerns the node's overall cross-system importance regardless of which layer paths use.
Can I compare multilayer betweenness scores across different networks?
Only after normalization that accounts for network size, number of layers, and density. Raw scores are sensitive to all these structural parameters, so cross-network comparisons without normalization are misleading.
Sources
- De Domenico, M., Solé-Ribalta, A., Cozzo, E., Kivelä, M., Moreno, Y., Porter, M. A., Gómez, S., & Arenas, A. (2013). Mathematical formulation of multilayer networks. Physical Review X, 3(4), 041022. DOI: 10.1103/PhysRevX.3.041022 ↗
- Kivelä, 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 ↗
How to cite this page
ScholarGate. (2026, June 3). Multilayer Betweenness Centrality (Tensor-based Network Centrality). ScholarGate. https://scholargate.app/en/network-analysis/multilayer-betweenness-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.
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- Multilayer Closeness CentralityNetwork analysis↔ compare
- Multilayer Community DetectionNetwork analysis↔ compare
- Multilayer Degree CentralityNetwork analysis↔ compare
- Multiplex Network AnalysisNetwork analysis↔ compare