Growing scale-free simplices

Kiriil Kovalenko, Irene Sendiña-Nadal, Nagi Khalil, Alex Dainiak, Daniil Musatov, Andrei M. Raigorodskii, Karin Alfaro-Bittner, Baruch Barzel, Stefano Boccaletti

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


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.

Original languageEnglish
Article number43
JournalCommunications Physics
Issue number1
StatePublished - Dec 2021

Bibliographical note

Funding Information:
I.S.-N. acknowledges support from the Ministerio de Economía, Industria y Competiti-vidad, Spain, under project FIS2017-84151-P. The work of A.M.R. and D.M. was supported by the Russian Federation Government (Grant number 075-15-2019-1926).

Publisher Copyright:
© 2021, The Author(s).


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