Related papers: IntComplex for high-order interactions

The ability to reason with and integrate different sensory inputs is the foundation underpinning human intelligence and it is the reason for the growing interest in modelling multi-modal information within Knowledge Graphs. Multi-Modal…

This paper develops a unified framework for measuring concentration in weighted systems embedded in networks of interactions. While traditional indices such as the Herfindahl-Hirschman Index capture dispersion in weights, they neglect the…

Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relations among arbitrary numbers of units through representations…

The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…

Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…

Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields. Its key mathematical techniques include persistent homology and the…

Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems…

Homophily is the seemingly ubiquitous tendency for people to connect and interact with other individuals who are similar to them. This is a well-documented principle and is fundamental for how society organizes. Although many social…

Psychiatric disorders have been traditionally conceptualized as latent conditions producing observable symptoms, but recent studies suggest that psychopathology may emerge from symptoms interactions. Psychometric networking model these…

Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding…

A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…

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…

Imitation is a basic updating mechanism for strategy evolution in structured populations, determining how individuals sample social information and translate it into behavioral changes. Higher-order networks, such as hypergraphs, generalize…

Topological landscape is introduced for networks with functions defined on the nodes. By extending the notion of gradient flows to the network setting, critical nodes of different indices are defined. This leads to a concise and…

Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions cannot be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods…

Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…

This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a…

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…

Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…

An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…