Higher-Order Networks and Hypergraphs

Traditional net­work models cap­tu­re pair­wi­se inte­rac­tions bet­ween enti­ties, but many real-world systems invol­ve group inte­rac­tions that go beyond sim­ple edges. Examples ran­ge from scien­ti­fic col­la­bo­ra­tions with mul­ti­ple co-authors, to bio­che­mi­cal reac­tions invol­ving seve­ral mole­cu­les, to group con­ver­sa­tions in social set­tings. These higher-order inte­rac­tions are natu­ral­ly mode­led with hyper­gra­phs and rela­ted struc­tu­res, which extend net­work scien­ce beyond the pair­wi­se paradigm.

In col­la­bo­ra­tion with Francesco Lotito (PhD, University of Trento, co-advi­sed with Federico Battiston), we have con­tri­bu­ted to the metho­do­lo­gi­cal foun­da­tions of higher-order net­work ana­ly­sis. Our work spans seve­ral directions:

  • Motif ana­ly­sis in hyper­gra­phs. We deve­lo­ped exact and sam­pling algo­ri­thms to detect over­re­pre­sen­ted pat­terns of higher-order inte­rac­tions, exten­ding the clas­sic notion of net­work motifs [CP22] [SC24] .

  • Hyperlink com­mu­ni­ties. We intro­du­ced a fra­mework to unco­ver meso­sca­le struc­tu­res in hyper­gra­phs, cap­tu­ring hie­rar­chi­cal orga­ni­za­tion and over­lap­ping com­mu­ni­ties [CN24].

  • Directed and mul­ti­plex hyper­gra­phs. We pro­po­sed mea­su­res for reci­pro­ci­ty, motif ana­ly­sis, and mul­ti­layer con­nec­ti­vi­ty in systems with direc­ted or mul­ti­plex higher-order interactions.

  • Software and data. We crea­ted Hypergraphx, one of the lea­ding Python libra­ries for higher-order net­work ana­ly­sis, and con­tri­bu­ted to Hypergraph-data, a cura­ted repo­si­to­ry of real-world hyper­gra­ph data­se­ts [JCN23] .

[CP22]   Quintino Francesco Lotito, Federico Musciotto, Alberto Montresor, and Federico Battiston. Higher-order motif ana­ly­sis in hyper­gra­phs. Communications Physics, 5(1):79, 2022. ISBN 2399–3650. [PDF], [Bibtex].

[JCN23]   Quintino Francesco Lotito, Martina Contisciani, Caterina De Bacco, Leonardo Di Gaetano, Luca Gallo, Alberto Montresor, Federico Musciotto, Nicolò Ruggeri, and Federico Battiston. Hypergraphx: a libra­ry for higher-order net­work ana­ly­sis. Journal of Complex Networks, 11(3), May 2023. [PDF], [Bibtex].

[SC24]   Quintino Francesco Lotito, Federico Musciotto, Federico Battiston, and Alberto Montresor. Exact and sam­pling methods for mining higher-order motifs in lar­ge hyper­gra­phs. Springer Computing, pages 475–494, February 2024. [PDF], [Bibtex].

[CN24]   Quintino Francesco Lotito, Federico Musciotto, Alberto Montresor, and Federico Battiston. Hyperlink com­mu­ni­ties in higher-order net­works. J. Complex Networks, 12(2), April 2024. [PDF], [Bibtex].

[ANS24]   Quintino Francesco Lotito, Alberto Montresor, and Federico Battiston. Multiplex mea­su­res for higher-order net­works. Applied Network Science, 9(55), September 2024. [PDF] , [Bibtex] .

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