Related papers: Structural reducibility of hypergraphs

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…

Hypergraphs provide a natural way of representing group relations, whose complexity motivates an extensive array of prior work to adopt some form of abstraction and simplification of higher-order interactions. However, the following…

A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order…

Networks provide an informative, yet non-redundant description of complex systems only if links represent truly dyadic relationships that cannot be directly traced back to node-specific properties such as size, importance, or coordinates in…

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…

The Hessian of a neural network captures parameter interactions through second-order derivatives of the loss. It is a fundamental object of study, closely tied to various problems in deep learning, including model design, optimization, and…

Higher-order networks effectively represent complex systems with group interactions. Existing methods usually overlook the relative contribution of group interactions (hyperlinks) of different sizes to the overall network structure. Yet,…

Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…

To better understand the structure and function of complex systems, researchers often represent direct interactions between components in complex systems with networks, assuming that indirect influence between distant components can be…

Graph Neural Networks (GNNs) have emerged as powerful tools for learning representations of graph-structured data, demonstrating remarkable performance across various tasks. Recognising their importance, there has been extensive research…

Graph matching pairs corresponding nodes across two or more graphs. The problem is difficult as it is hard to capture the structural similarity across graphs, especially on large graphs. We propose to incorporate high-order information for…

Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…

Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…

In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…

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…

Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…

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…

The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern the formation and evolution…

Many real world systems need to operate on heterogeneous information networks that consist of numerous interacting components of different types. Examples include systems that perform data analysis on biological information networks; social…

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…