Related papers: Measuring dynamical systems on directed hyper-grap…
Disease spreading models such as the ubiquitous SIS compartmental model and its numerous variants are widely used to understand and predict the behaviour of a given epidemic or information diffusion process. A common approach to imbue more…
Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…
We propose a one parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We show that for each value of the parameter the resulting process…
Many real-world interactions (e.g., researcher collaborations and email communication) occur among multiple entities. These group interactions are naturally modeled as hypergraphs. In graphs, transitivity is helpful to understand the…
Networks are a powerful tool to model the structure and dynamics of complex systems across scales. Direct connections between system components are often represented as edges, while paths and walks capture indirect interactions. This…
Many systems, ranging from biological and engineering systems to social systems, can be modeled as directed networks, with links representing directed interaction between two nodes. To assess the importance of a node in a directed network,…
Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches,…
The central points of communication network flow has often been identified using graph theoretical centrality measures. In real networks, the state of traffic density arises from an interplay between the dynamics of the flow and the…
Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…
Centrality measures identify and rank the most influential entities of complex networks. In this paper, we generalize matrix function-based centrality measures, which have been studied extensively for single-layer and temporal networks in…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social…
Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
As the complexity of production processes increases, the diversity of data types drives the development of network monitoring technology. This paper mainly focuses on an online algorithm to detect serially correlated directed networks…
We study a graph-theoretic approach to the $\mathcal{H}_{\infty}$ performance of leader following consensus dynamics on directed and undirected graphs. We first provide graph-theoretic bounds on the system $\mathcal{H}_{\infty}$ norm of the…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
We present a general framework that enables one to model high-order interaction among entangled dynamical systems, via hypergraphs. Several relevant processes can be ideally traced back to the proposed scheme. We shall here solely elaborate…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…