Related papers: Graphs are maximally expressive for higher-order i…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically…

Hypergraph representations are both more efficient and better suited to describe data characterized by relations between two or more objects. In this work, we present a new graph neural network based on message passing capable of processing…

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…

Hypergraphs generalize classical graphs by allowing a single edge to connect multiple vertices, providing a natural language for modeling higher-order interactions. Superhypergraphs extend this paradigm further by accommodating nested,…

Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the…

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 network science, collective dynamics of complex systems are typically modelled as (nonlinear, often including many-body) vertex-level update rules evolving over a graph interaction structure. In recent years, frameworks that explicitly…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…

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…

Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…

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…

We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…

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…

What kind of macroscopic structural and dynamical patterns can we observe in real-world hypergraphs? What can be underlying local dynamics on individuals, which ultimately lead to the observed patterns, beyond apparently random evolution?…

Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in…

Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…

In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the…