Related papers: Structural reducibility of hypergraphs
We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
Looking to overcome the limitations of traditional networks, the network science community has lately given much attention to the so-called higher-order networks, where group interactions are modeled alongside pairwise ones. While degree…
Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics,…
Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications,…
All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
A relational structure $\mathbb{X}$ is called reversible iff each bijective homomorphism from $\mathbb{X}$ onto $\mathbb{X}$ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible…
Graphs depict pairwise relationships between objects within a system. Higher-order interactions (HOIs), which involve more than two objects simultaneously, are common in nature. Such interactions can change the stability of a complex…
A complex system with many interacting individuals can be represented by a network consisting of nodes and links representing individuals and pairwise interactions, respectively. However, real-world systems grow with time and include many…
Extending community detection from pairwise networks to hypergraphs introduces fundamental theoretical challenges. Hypergraphs exhibit structural heterogeneity with no direct graph analogue: hyperedges of varying orders can connect nodes…
Many empirical systems contain complex interactions of arbitrary size, representing, for example, chemical reactions, social groups, co-authorship relationships, and ecological dependencies. These interactions are known as higher-order…
Social relationships (e.g., friends, couple etc.) form the basis of the social network in our daily life. Automatically interpreting such relationships bears a great potential for the intelligent systems to understand human behavior in…
Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…
The description of the dynamics of complex systems, in particular the capture of the interaction structure and causal relationships between elements of the system, is one of the central questions of interdisciplinary research. While the…
Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…
Understanding human mobility is essential for applications ranging from urban planning to public health. Traditional mobility models such as flow networks and colocation matrices capture only pairwise interactions between discrete…
Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…