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The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
Temporal Graph Neural Networks (TGNNs) have gained growing attention for modeling and predicting structures in temporal graphs. However, existing TGNNs primarily focus on pairwise interactions while overlooking higher-order structures that…
Many networks can be characterised by the presence of communities, which are groups of units that are closely linked. Identifying these communities can be crucial for understanding the system's overall function. Recently, hypergraphs have…
What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct…
Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within…
Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of…
Dynamic systems that consist of a set of interacting elements can be abstracted as temporal networks. Recently, higher-order patterns that involve multiple interacting nodes have been found crucial to indicate domain-specific laws of…
Individuals interact and cooperate in structured systems. Many studies represent this structure using static networks, where each link represents a permanent connection between two nodes. However, real interactions are generally not…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
We consider a heteroclinic network in the framework of winnerless competition of species. It consists of two levels of heteroclinic cycles. On the lower level, the heteroclinic cycle connects three saddles, each representing the survival of…
An increasing number of complex systems are now modeled as networks of coupled dynamical entities. Nonlinearity and high-dimensionality are hallmarks of the dynamics of such networks but have generally been regarded as obstacles to control.…
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
Networks are important structures used to model complex systems where interactions take place. In a basic network model, entities are represented as nodes, and interaction and relations among them are represented as edges. However, in a…
The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
In this chapter, we derive and analyse models for consensus dynamics on hypergraphs. As we discuss, unless there are nonlinear node interaction functions, it is always possible to rewrite the system in terms of a new network of effective…
Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually…
The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…
Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific…