2022/07/21 by Fabio Saracco, Saracco, Fabio, Giovanni Petri +5
Biochemistry, Genetics and Molecular Biology · Neuroscience · Physics and Astronomy · #Bioinformatics and Genomic Networks #Complex Network Analysis Techniques #Data Analysis #FOS: Computer and information sciences #FOS: Physical sciences #Functional Brain Connectivity Studies #Social and Information Networks (cs.SI) #Statistical Mechanics (cond-mat.stat-mech) #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2207.12123
openalex publication_date 2022/07/21 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Network theory has often disregarded many-body relationships, solely focusing on pairwise interactions: neglecting them, however, can lead to misleading representations of complex systems. Hypergraphs represent a suitable framework for describing polyadic interactions. Here, we leverage the representation of hypergraphs based on the incidence matrix for extending the entropy-based approach to higher-order structures: in analogy with the Exponential Random Graphs, we introduce the Exponential Random Hypergraphs (ERHs). After exploring the asymptotic behaviour of thresholds generalising the percolation one, we apply ERHs to study real-world data. First, we generalise key network metrics to hypergraphs; then, we compute their expected value and compare it with the empirical one, in order to detect deviations from random behaviours. Our method is analytically tractable, scalable and capable of revealing structural patterns of real-world hypergraphs that differ significantly from those emerging as a consequence of simpler constraints.