Related papers: Higher-order Connection Laplacians for Directed Si…

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…

Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…

The propagation of information in social, biological and technological systems represents a crucial component in their dynamic behavior. When limited to pairwise interactions, a rather firm grip is available on the relevant parameters and…

Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory,…

Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes…

Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…

Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of…

Non-reciprocal interactions play a crucial role in many social and biological complex systems. While directionality has been thoroughly accounted for in networks with pairwise interactions, its effects in systems with higher-order…

Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant…

Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or…

Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…

Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize social contagion processes such as opinion…

The human brain is a complex system defined by multi-way, higher-order interactions invisible to traditional pairwise network models. Although a diverse array of analytical methods has been developed to address this shortcoming, the field…

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…

Higher-order interactions have recently emerged as a promising framework for describing new dynamical phenomena in heterogeneous contagion processes. However, a fundamental open question is how to understand their contribution from the…

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…

Despite the recent successes of vanilla Graph Neural Networks (GNNs) on various tasks, their foundation on pairwise networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this…

Laplacian dynamics on a signless graph characterize a class of linear interactions, where pairwise cooperative interactions between all agents lead to the convergence to a common state. On a structurally balanced signed graph, the agents…

Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…

Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral properties of the…