Related papers: Hypergraph Laplacians in Diffusion Framework

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…

Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…

Due to the advantages of hypergraphs in modeling high-order relationships in complex systems, they have been applied to higher-order clustering, hypergraph neural networks and computer vision. These applications rely heavily on access to…

Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…

Quantifying the relations (e.g., similarity) between complex networks paves the way for studying the latent information shared across networks. However, fundamental relation metrics are not well-defined between networks. As a compromise,…

We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These sheaf neural networks are based on the sheaf Laplacian, a generalization of the graph…

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…

Reasoning about objects, relations, and physics is central to human intelligence, and a key goal of artificial intelligence. Here we introduce the interaction network, a model which can reason about how objects in complex systems interact,…

Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits.…

Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions…

High-level classification algorithms focus on the interactions between instances. These produce a new form to evaluate and classify data. In this process, the core is the complex network building methodology because it determines the…

Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the…

Opinion dynamics is a central subject of computational social science, and various models have been developed to understand the evolution and formulation of opinions. Existing models mainly focus on opinion dynamics on graphs that only…

Transformer architectures, capable of capturing sequential dependencies in the history of user interactions, have become the dominant approach in sequential recommender systems. Despite their success, such models consider sequence elements…

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…

The development of simple and fast hypergraph spectral methods has been hindered by the lack of numerical algorithms for simulating heat diffusions and computing fundamental objects, such as Personalized PageRank vectors, over hypergraphs.…

We present a new feature extraction method for complex and large datasets, based on the concept of transport operators on graphs. The proposed approach generalizes and extends the many existing data representation methodologies built upon…

Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this…

Graph Laplacians as well as related spectral inequalities and (co-)homology provide a foray into discrete analogues of Riemannian manifolds, providing a rich interplay between combinatorics, geometry and theoretical physics. We apply some…