Agenda
Histórico

11 de maio de 2026
14h00
Sala F-210 (IFSC-USP)

Silvio C. Ferreira
Departamento de Física
Universidade Federal de Viçosa

Nesting Controls Phase Transitions in Higher-Order Contagion

Higher-order networks describe many-body interactions, where collective group dynamics fundamentally differ from pairwise interactions [1]. These systems exhibit phenomena absent in pairwise models, such as catastrophic activation, hysteresis, and hybrid transitions. Higher-order interactions can be formalized as Simplicial Complexes (SCs) or Hypergraphs (HGs), with SCs representing cases where every higher-order interaction includes all lower-order subsets [1]. We study how contagion dynamics differ between SCs and HGs using the nesting coefficient [2] that quantifies how lower-order interactions are embedded within higher-order ones, defining a continuum between simplicial complexes and random hypergraphs. Using a higher-order susceptible-infected-susceptible model, we show that increasing nesting lowers the activation threshold and suppresses discontinuous transitions, while weak embedding favors explosive behavior. We further demonstrate that correlations between nesting and interaction order modulate the onset of activity while only weakly affecting transition discontinuity. Analysis of synthetic and empirical networks reveals that nesting strongly predicts hysteresis, establishing it as a key structural determinant of phase transitions in higher-order systems. Large-scale simulations rely on optimized algorithms [3] for realistic networks.

[1] F Battiston et al., "The physics of higher-order interactions in complex systems," Nature Physics, vol. 17, no. 10, pp. 1093-1098, 2021.
[2] HP Maia, GF de Arruda, SC Ferreira, Y Moreno, "Nesting Controls Phase Transitions in Higher-Order Contagion," arXiv:2604.23337, 2026.
[3] HP Maia, W Cota, Y Moreno, SC Ferreira, "Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks," arXiv:2509.2017, 2025.