Federico Battiston, Giulia Cencetti, Iacopo Iacopini, Vito Latora, Maxime Lucas, Alice Patania, et al. (8 authors; also Jean-Gabriel Young, Giovanni Petri) (2020), Physics Reports 874, 1–92 (2020) — ARXIV-2006.01764
Key takeaways
- Many systems’ interactions happen in groups rather than pairs. Representing them explicitly, as hypergraphs or simplicial complexes, changes both the measured structure and the dynamics, and in particular adds new non-linearities and abrupt (explosive) transitions that pairwise models miss.
Seeded from the abstract and a skim, before the reading in NOTE-057. What follows is what the work says about itself.
The review argues that in social contact, chemical reactions, ecology and elsewhere, interactions involve three or more units and cannot be reduced to dyads. It surveys the new field of networks with higher-order interactions. It first relates the frameworks used to represent them, then covers structural measures and generative models (random and growing simplicial complexes, bipartite graphs, hypergraphs). It then turns to dynamics: diffusion, synchronization, spreading, opinion dynamics and evolutionary games on higher-order structures, followed by applications and open problems.
Standing in the record
Filed from the survey of 2026-09-25 of work the anthology set aside as out of scope (tier C): 440 seconds of active reading over 2 sessions in the papers-feed tracker. It was filed Deferred, unread. NOTE-057 is the close reading of 2026-09-25, and it placed the work: Active — the standard entry point to higher-order network science, worth reading for §II–§III (definitions and operators) and as a map of the 2020 literature. Read it for definitions and pointers, not as evidence: the dynamical claims are one-paper summaries, several formulas carry typos (listed below), and the conclusion’s “profoundly change” list includes linear cases that §V itself shows reduce to pairwise.
When seeded, before the reading in NOTE-057, the entry gave a priority for a deeper reading: medium — A load-bearing reference, and the owner’s time is moderate (t=440 s over 2 sessions). The skim captures the map of the field; depth is only needed for whichever section a note cites.
What the seeding asked a deeper reading to check (NOTE-057 is that reading):
- This is the standard reference for higher-order networks, and the natural anchor citation for a network-science note on hypergraphs and simplicial complexes. It is also relevant background for hypergraph and simplicial neural networks, which the review predates.
- Being a 92-page review, it is best read by section on demand rather than end to end.
Access when seeded: I read the arXiv abstract page (v1 2 Jun 2020) and the full arXiv PDF (109 pp.). I read the abstract, the table of contents and §X (Outlook and conclusions), and skimmed section heads throughout. Crossref gives the Physics Reports record (created 2020-06-13, issue August 2020). The arXiv title writes “structure and dynamics” in lower case; the title above is the journal’s.