https://doi.org/10.1140/epjds/s13688-025-00577-3
Research
The relevance of higher-order ties
Leiden Institute of Advanced Computer Science (LIACS), Leiden University, Einsteinweg 55, 2333 CC, Leiden, The Netherlands
a
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Received:
5
December
2024
Accepted:
18
July
2025
Published online:
21
August
2025
Higher-order networks effectively represent complex systems with group interactions. Existing methods usually overlook the relative contribution of group interactions (hyperedges) of different sizes to the overall network structure. Yet, this has many important applications, especially when the network has meaningful node labels. In this work, we propose a methodology to precisely measure the contribution of different orders to topological network properties. First, we propose the order contribution measure, which quantifies the contribution of hyperedges of different orders to the link weights (local scale), number of triangles (mesoscale) and size of the largest connected component (global scale) of the pairwise weighted network. Second, we propose the measure of order relevance, which gives insights in how hyperedges of different orders contribute to the considered network property. Most interestingly, it enables an assessment of whether this contribution is synergistic or redundant with respect to that of hyperedges of other orders. Third, to account for labels, we propose a metric of label group balance to assess how hyperedges of different orders connect label-induced groups of nodes. We applied these metrics to a large-scale board interlock network and scientific collaboration network, in which node labels correspond to geographical location of the nodes. Experiments including a comparison with randomized null models reveal how from the global level perspective, we observe synergistic contributions of orders in the board interlock network, whereas in the collaboration network orders contribute more redundantly. The findings shed new light on social scientific debates on the role of busy directors in global business networks and the connective effects of large author teams in scientific collaboration networks.
Key words: Higher-order networks / Network measures / Socio-economic networks / Scientific collaboration networks
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjds/s13688-025-00577-3.
© The Author(s) 2025
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