All beauty, richness and harmony in the emergent dynamics of a complex system largely
depend on the specific way in which its elementary components interact. The last twenty-five …

Network science has evolved into an indispensable platform for studying complex systems.
But recent research has identified limits of classical networks, where links connect pairs of …

Complex networks have become the main paradigm for modelling the dynamics of
interacting systems. However, networks are intrinsically limited to describing pairwise …

The complexity of many biological, social and technological systems stems from the richness
of the interactions among their units. Over the past decades, a variety of complex systems …

Hypergraphs have attracted increasing attention in recent years thanks to their flexibility in
naturally modeling a broad range of systems where high-order relationships exist among …

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 …

Simplicial complexes describe the simple fact that in social networks a link can connect
more than two individuals. As we show here, this has far-reaching consequences for …

Higher-order networks have emerged as a powerful framework to model complex systems
and their collective behavior. Going beyond pairwise interactions, they encode structured …

Gathering events, eg, going to gyms and meetings, are ubiquitous and crucial in the
spreading phenomena, which induce higher-order interactions, and thus can be described …

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 …