Related papers: Simplicial degree in complex networks. Application…
Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…
Persistent homology has been studied to better understand the structural properties and topology features of weighted networks. It can reveal hidden layers of information about the higher-order structures formed by non-pairwise interactions…
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…
Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…
Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…
In this tutorial, we provide a didactic treatment of the emerging topic of signal processing on higher-order networks. Drawing analogies from discrete and graph signal processing, we introduce the building blocks for processing data on…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
Directed graphs are ubiquitous models for networks, and topological spaces they generate, such as the directed flag complex, have become useful objects in applied topology. The simplices are formed from directed cliques. We extend Atkin's…
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…
Graph machine learning methods excel at leveraging pairwise relations present in the data. However, graphs are unable to fully capture the multi-way interactions inherent in many complex systems. An effective way to incorporate them is to…
A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. Many multicomponent interactions can be grasped through simplicial complexes, which have recently…
Multilayer networks provide a more advanced and comprehensive framework for modeling real-world systems compared to traditional single-layer and multiplex networks. Unlike single-layer models, multilayer networks have multiple interacting…
Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly…
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…
Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a…
Multiplex networks describe systems whose interactions can be of different nature, and are fundamental to understand complexity of networks beyond the framework of simple graphs. Recently it has been pointed out that restricting the…
Simplicial neural networks (SNN) have recently emerged as the newest direction in graph learning which expands the idea of convolutional architectures from node space to simplicial complexes on graphs. Instead of pre-dominantly assessing…
We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
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,…