Related papers: Beyond directed hypergraphs: heterogeneous hypergr…

Graphs (i.e., networks) have become an integral tool for the representation and analysis of relational data. Advances in data gathering have lead to multi-relational data sets which exhibit greater depth and scope. In certain cases, this…

There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…

Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…

Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is…

In this paper some results about the controllability of spectral centrality in a complex network are presented. In particular, the inverse problem of designing an unweigthed graph with a prescribed centrality is considered, by showing that…

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…

In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such…

Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure 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 scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…

We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a.…

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 perspective derives its success from the relative simplicity…

The growing interest in hypergraph neural networks (HGNNs) is driven by their capacity to capture the complex relationships and patterns within hypergraph structured data across various domains, including computer vision, complex networks,…

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…

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

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 network analysis uses the ideas of hypergraphs, simplicial complexes, multilinear and tensor algebra, and more, to study complex systems. These are by now well established mathematical abstractions. What's new is that the ideas…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

Identifying the most influential nodes in networked systems is of vital importance to optimize their function and control. Several scalar metrics have been proposed to that effect, but the recent shift in focus towards network structures…