Learning Resources

Hypergraphs and simplicial complexes in focus: a roadmap for future research in higher-order interactions

1/4/2026

Publication

Emergent Higher-Order Structure from Fast Adaptive Networks

19/3/2026

Publication

Group adaptation drives opinion dynamics in higher-order networks

23/2/2026

Publication

Higher-order dissimilarity measures for hypergraph comparison

20/2/2026

Publication

Simplicial Complex Emergence on Directed Hypergraphs

2/12/2025

Publication

Spectral theory of dense hypergraph limits

6/11/2025

Publication

Course: Spectral Theory of Graphs and Hypergraphs

This course by BeyondTheEdge researcher Raffaella Mulas gives an introduction to the spectral theory of graphs and hypergraphs.

24/9/2025

Tutorial

BeyondTheEdge Course: Spectral Theory of Graphs and Hypergraphs

Decoding how higher-order network interactions shape contagion dynamics

Bifurcation theory gives insights how higher-order network interactions affect complex contagion dynamics.

19/8/2025

Publication

Higher-order interactions give complex contagion

Unraveling high-order interactions in electrophysiological brain signals using elliptical distributions: Moving beyond the Gaussian approximation

BeyondTheEdge output on high-order interactions in electrophysiological brain signals using elliptical distributions

2/5/2025

Publication

Higher-order dissimilarity measures for hypergraph comparison

BeyondTheEdge research output on hypergraph comparison

21/3/2025

Publication

Bear Networks

The mathematics of networks introduced by soccer loving bears.

14/5/2024

Publication

What Are Higher-Order Networks?

In this overview article, the authors explain what higher-order networks are, why they may be important, and how they influence dynamics.

8/8/2023

Publication

BeyondTheEdge Supervision Guidelines

For the supervision of PhD students

25/3/2024

Publication

Seminar: Stefano Boccaletti

The six degrees of separation: science or a myth?

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Our Courses: Higher-Order networks explained

In the course "Higher-Order Interaction Networks—An Introduction" BeyondTheEdge researcher Michael Schaub gives an overview of the topic of higher-order networks and dynamics. This course provides the ideal starting point for future researchers in the field. All material is available for free through the BeyondTheEdge website.

BeyondTheEdge Course

Introductory Reading

These references provide an introduction to higher-order networks and dynamics from mathematical and physical viewpoints.

What are higher-order networks?

C. Bick, E. Gross, H. A. Harrington, M. T. Schaub. SIAM Review 65, 686–731 (2023). doi:10.1137/21M1414024 [Open Access]

Higher-Order Networks: An introduction to simplicial complexes

G. Bianconi. Cambridge University Press

The physics of higher-order interactions in complex systems

F. Battiston et al. Nat. Phys. 17, 1093–1098 (2021). doi:10.1038/s41567-021-01371-4F

Networks beyond pairwise interactions: Structure and dynamics

F. Battiston et al. Physics Reports 874, 1–92 (2020). doi:10.1016/j.physrep.2020.05.004

Learning resources