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In various application areas, networked data is collected by measuring interactions involving some specific set of core nodes. This results in a network dataset containing the core nodes along with a potentially much larger set of fringe…
We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…
Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of…
Hypergraphs have been a powerful tool to represent higher-order interactions, where hyperedges can connect an arbitrary number of nodes. Quantifying the relative importance of nodes and hyperedges in hypergraphs is a fundamental problem in…
The analysis of complex and time-evolving interactions like social dynamics represents a current challenge for the science of complex systems. Temporal networks stand as a suitable tool to schematise such systems, encoding all the appearing…
Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to…
Many networked datasets with units interacting in groups of two or more, encoded with hypergraphs, are accompanied by extra information about nodes, such as the role of an individual in a workplace. Here we show how these node attributes…
Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph…
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…
Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…
Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics…
Decomposing a graph into a hierarchical structure via $k$-core analysis is a standard operation in any modern graph-mining toolkit. $k$-core decomposition is a simple and efficient method that allows to analyze a graph beyond its mere…
Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem…
Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…
Individuals interact and cooperate in structured systems. Many studies represent this structure using static networks, where each link represents a permanent connection between two nodes. However, real interactions are generally not…
Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…
Key graph-based problems play a central role in understanding network topology and uncovering patterns of similarity in homogeneous and temporal data. Such patterns can be revealed by analyzing communities formed by nodes, which in turn can…
Learning from structured data is a core machine learning task. Commonly, such data is represented as graphs, which normally only consider (typed) binary relationships between pairs of nodes. This is a substantial limitation for many domains…
Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…
Modeling higher-order interactions (HOI) has emerged as a crucial challenge in complex systems analysis, as many phenomena cannot be fully captured by pairwise relationships alone. Hypergraphs, which generalize graphs by allowing…