Related papers: Connected components in networks with higher-order…

Complex systems, such as economic, social, biological, and ecological systems, usually feature interactions not only between pairwise entities but also among three or more entities. These multi-entity interactions are known as higher-order…

A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such…

In this work, we propose a comprehensive theoretical framework combining percolation theory with nonlinear dynamics in order to study hypergraphs with a time-varying giant component. We consider in particular hypergraphs with higher-order…

A directed graph G (V, E) is strongly connected if and only if, for a pair of vertices X and Y from V, there exists a path from X to Y and a path from Y to X. In Computer Science, the partition of a graph in strongly connected components is…

We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…

We propose a method for obtaining parsimonious decompositions of networks into higher order interactions which can take the form of arbitrary motifs.The method is based on a class of analytically solvable generative models, where vertices…

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…

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…

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 more agents at a time. These data are better described by…

One of the defining features of complex networks is the connectivity properties that we observe emerging from local interactions. Recently, hypergraphs have emerged as a versatile tool to model networks with non-dyadic, higher-order…

There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…

Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by…

Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to…

Higher-order interactions play a key role for the stability and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of…

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…

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…

Higher-order information is crucial for relational learning in many domains where relationships extend beyond pairwise interactions. Hypergraphs provide a natural framework for modeling such relationships, which has motivated recent…

Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…

The microscopic organization of dynamical systems coupled via higher-order interactions plays a pivotal role in understanding their collective behavior. In this paper, we introduce a framework for systematically investigating the impact of…