Related papers: Pangraphs as models of higher-order interactions

Being cognizant of the abundance of multi-body interactions in various complex systems, here we investigate a possible way to incorporate multi-body interactions in dynamical networks. Adopting hypergraph as the underlying architecture aids…

Finding inherent or processed links within a dataset allows to discover potential knowledge. The main contribution of this article is to define a global framework that enables optimal knowledge discovery by visually rendering co-occurences…

Localization behaviours of Laplacian eigenvectors of complex networks provide understanding to various dynamical phenomena on the corresponding complex systems. We numerically investigate role of hyperedges in driving eigenvector…

The ongoing need for effective epidemic modeling has driven advancements in capturing the complex dynamics of infectious diseases. Traditional models, such as Susceptible-Infected-Recovered, and graph-based approaches often fail to account…

The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve…

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…

We define a higher order Deffuant model by generalizing the original pairwise interaction model for bounded-confidence opinion-dynamics to interactions involving a group of agents of size k. The generalized model is naturally encoded in a…

Interactions involving multiple objects simultaneously are ubiquitous across many domains. The systems these interactions inhabit can be modelled using hypergraphs, a generalization of traditional graphs in which each edge can connect any…

Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to…

Large language models (LLMs) have recently shown strong potential in modeling relational structures. However, existing approaches remain fundamentally graph-centric: they focus on processing pairwise graph structures into tokens that LLMs…

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…

Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks are not always restricted to binary interactions but often include higher-order interactions among the nodes. These…

Molecular interactions have widely been modelled as networks. The local wiring patterns around molecules in molecular networks are linked with their biological functions. However, networks model only pairwise interactions between molecules…

Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce…

Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

Theoretical and computational frameworks of modern science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal operations of two arguments in mathematical models, limits our capacity…

Graphs are widely used to encapsulate a variety of data formats, but real-world networks often involve complex node relations beyond only being pairwise. While hypergraphs and hierarchical graphs have been developed and employed to account…

Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and…

Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…