Network-based modeling of complex systems and data using the language of graphs has
become an essential topic across a range of different disciplines. Arguably, this graph-based …

In this tutorial, we provide a didactic treatment of the emerging topic of signal processing on
higher-order networks. Drawing analogies from discrete and graph signal processing, we …

A deluge of new data on real-world networks suggests that interactions among system units
are not limited to pairs, but often involve a higher number of nodes. To properly encode …

The message passing framework is the foundation of the immense success enjoyed by
graph neural networks (GNNs) in recent years. In spite of its elegance, there exist many …

We consider the construction of neural network architectures for data on simplicial
complexes. In studying maps on the chain complex of a simplicial complex, we define three …

Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide
a promising way to model higher-order relations in data and further solve relevant prediction …

Recent empirical evidence has shown that in many real-world systems, successfully
represented as networks, interactions are not limited to dyads, but often involve three or …

We investigate consensus dynamics on temporal hypergraphs that encode network systems
with time-dependent, multiway interactions. We compare these consensus processes with …

Digital communication has made the public discourse considerably more complex, and new
actors and strategies have emerged as a result of this seismic shift. Aside from the often …

Dynamical systems on hypergraphs can display a rich set of behaviors not observable for
systems with pairwise interactions. Given a distributed dynamical system with a putative …