Multilayer Degree Centrality
Multilayer Degree Centrality (Aggregated and Layer-Specific Node Importance in Multilayer Networks) · Also known as: multilayer degree, multiplex degree centrality, overlapping-layer degree centrality, MDC
Multilayer degree centrality extends the classic degree centrality measure to networks composed of multiple layers — such as networks representing different types of social ties, communication channels, or relationship contexts simultaneously. It quantifies how many connections a node has across one or all layers, revealing nodes that are influential not just in a single context but across the entire multi-relational structure.
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When to use it
Use multilayer degree centrality when your network data has distinct relationship types or interaction channels that should not be collapsed into a single weighted edge — for instance, social ties across multiple platforms, transportation modes in a city, or different types of biological interactions. It is appropriate when you want to rank nodes by overall activity or influence across all layers and when single-layer degree would miss nodes that are moderately connected in many layers but not dominant in any one. Avoid it when you have only one type of relationship (use plain degree centrality instead), when the number of observations per layer is very small (centrality estimates become unstable), or when layers are not meaningfully comparable and aggregation would be misleading.
Strengths & limitations
- Directly extends the well-understood degree centrality concept to multi-relational data without requiring fundamentally new intuitions.
- Captures nodes that are broadly active across many layers, which single-layer analysis systematically misses.
- Computationally lightweight: aggregating degree across layers scales linearly in edges and layers.
- Layer-specific degree profiles allow nuanced comparison — you can see not just total centrality but in which contexts a node is active.
- Compatible with both binary and weighted multilayer representations.
- Aggregation treats all layers as equally important by default; without explicit weighting, dominant layers can overwhelm the signal from smaller ones.
- Like plain degree centrality, it measures direct connections only and ignores structural position (paths, bridging, influence propagation).
- Interpretation is straightforward only when layers are conceptually comparable; mixing structurally incompatible layer types can produce misleading aggregate scores.
- Requires that the same node set appears across layers (multiplex assumption); missing or partial node coverage per layer needs explicit handling.
Frequently asked
How is multilayer degree centrality different from weighted degree centrality?
Weighted degree centrality sums edge weights within a single-layer network. Multilayer degree centrality operates on structurally distinct layers, each representing a different relationship type; aggregation happens across layers rather than across edge weights within one layer.
Should I weight layers differently when aggregating?
In the standard formulation layers are equally weighted, but if layers differ in theoretical importance or density, applying layer-specific weights before aggregation is appropriate and recommended. The choice of weights should be grounded in your research question, not chosen post-hoc to improve rankings.
What software can compute multilayer degree centrality?
The MuxViz platform (De Domenico et al.) is purpose-built for multilayer network analysis including degree centrality. Python libraries such as NetworkX (with manual layer looping) and pymnet also support multilayer centrality computations.
When should I use betweenness or eigenvector centrality instead?
Multilayer degree centrality is best for identifying broadly active or highly connected nodes. Use multilayer betweenness centrality when you care about nodes that bridge communities or control information flow, and multilayer eigenvector or PageRank variants when you want to weight connections by the importance of neighbors.
Is a node ranked high in aggregate always important in each layer?
Not necessarily. A node with moderate degree across many layers can outscore a node with very high degree in one layer. Always inspect per-layer profiles alongside the aggregate score to understand whether a node's centrality is broad or concentrated.
Sources
- 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 ↗
- 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 ↗
How to cite this page
ScholarGate. (2026, June 3). Multilayer Degree Centrality (Aggregated and Layer-Specific Node Importance in Multilayer Networks). ScholarGate. https://scholargate.app/en/network-analysis/multilayer-degree-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.
- Degree CentralityNetwork analysis↔ compare
- Multilayer Betweenness CentralityNetwork analysis↔ compare
- Multilayer Closeness CentralityNetwork analysis↔ compare
- Multilayer PageRankNetwork analysis↔ compare
- Multiplex Network AnalysisNetwork analysis↔ compare
- Weighted Degree CentralityNetwork analysis↔ compare