2023/01/05 by Carlos Zapata-Carratalá, Zapata-Carratalá, Carlos, Maximilian Schich +5
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Data Visualization and Analytics #FOS: Physical sciences #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph)
paper · pdf · doi:10.48550/arxiv.2301.07494
openalex publication_date 2023/01/05 · openalex created_date 2023/01/20 · openalex updated_date 2026/07/28
Theoretical and computational frameworks of modern science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal operations of two arguments in mathematical models, limits our capacity to faithfully capture irreducible polyadic interactions in higher-order systems. A paradigmatic example of a higher-order interaction is the Borromean link of three interlocking rings. In this paper we propose a mathematical framework via hypergraphs and hypermatrix algebras that allows to formalize such forms of higher-order bonding and connectivity in a parsimonious way. Our framework builds on and extends current techniques in higher-order networks -- still mostly rooted in binary structures such as adjacency matrices -- and incorporates recent developments in higher-arity structures to articulate the compositional behavior of adjacency hypermatrices. Irreducible higher-order interactions turn out to be a widespread occurrence across natural sciences and socio-cultural knowledge representation. We demonstrate this by reviewing recent results in computer science, physics, chemistry, biology, ecology, social science, and cultural analysis through the conceptual lens of irreducible higher-order interactions. We further speculate that the general phenomenon of emergence in complex systems may be characterized by spatio-temporal discrepancies of interaction arity.