Growing scale-free simplices

Kirill Kovalenko

doi:10.1038/s42005-021-00538-y

Growing scale-free simplices

2021-03-05

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DOI：10.1038/s42005-021-00538-y

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Higher-order networks including many-body interactions among nodes are ubiquitous in complex systems. The authors propose several growing mechanisms which are able to generate synthetic simplicial complexes displaying desired and customized statistical properties fitting those observed in the real world. The past two decades have seen significant successes in our understanding of networked systems, from the mapping of real-world networks to the establishment of generative models recovering their observed macroscopic patterns. These advances, however, are restricted to pairwise interactions and provide limited insight into higher-order structures. Such multi-component interactions can only be grasped through simplicial complexes, which have recently found applications in social, technological, and biological contexts. Here we introduce a model to grow simplicial complexes of order two, i.e., nodes, links, and triangles, that can be straightforwardly extended to structures containing hyperedges of larger order. Specifically, through a combination of preferential and/or nonpreferential attachment mechanisms, the model constructs networks with a scale-free degree distribution and an either bounded or scale-free generalized degree distribution. We arrive at a highly general scheme with analytical control of the scaling exponents to construct ensembles of synthetic complexes displaying desired statistical properties.

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