Related papers: Graphs are maximally expressive for higher-order i…
Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the…
Graph learning is a prevalent domain that endeavors to learn the intricate relationships among nodes and the topological structure of graphs. Over the years, graph learning has transcended from graph theory to graph data mining. With the…
Biomedical networks (or graphs) are universal descriptors for systems of interacting elements, from molecular interactions and disease co-morbidity to healthcare systems and scientific knowledge. Advances in artificial intelligence,…
Deep representation learning on non-Euclidean data types, such as graphs, has gained significant attention in recent years. Invent of graph neural networks has improved the state-of-the-art for both node and the entire graph representation…
Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…
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…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
Graphs serve as powerful tools for modeling pairwise interactions in diverse fields such as biology, material science, and social networks. However, they inherently overlook interactions involving more than two entities. Simplicial…
Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by…
The explosion of digital information and the growing involvement of people in social networks led to enormous research activity to develop methods that can extract meaningful information from interaction data. Commonly, interactions are…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Many complex systems that exhibit temporal non-pairwise interactions can be represented by means of generative higher-order network models. Here, we propose a hidden variables formalism to analytically characterize a general class of…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a…
We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of…
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…
While relations among individuals make an important part of data with scientific and business interests, existing statistical modeling of relational data has mainly been focusing on dyadic relations, i.e., those between two individuals.…
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…