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In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Understanding the internal dynamics of Recurrent Neural Networks (RNNs) is crucial for advancing their interpretability and improving their design. This study introduces an innovative information-theoretic method to identify and analyze…
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…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
While deep networks have been enormously successful over the last decade, they rely on flat-feature vector representations, which makes them unsuitable for richly structured domains such as those arising in applications like social network…
With the constant increase of the number of autonomous vehicles and connected objects, tools to understand and reproduce their mobility models are required. We focus on chaotic dynamics and review their applications in the design of…
Networks of dynamical systems play an important role in various domains and have motivated many studies on the control and analysis of linear dynamical networks. For linear network models considered in these studies, it is typically…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…
Networks are powerful tools for modeling interactions in complex systems. While traditional networks use scalar edge weights, many real-world systems involve multidimensional interactions. For example, in social networks, individuals often…
What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct…
Regular Path Queries (RPQs) are a type of graph query where answers are pairs of nodes connected by a sequence of edges matching a regular expression. We study the techniques to process such queries on a distributed graph of data. While…
A set of analytical and computational tools based on transition path theory (TPT) is proposed to analyze flows in complex networks. Specifically, TPT is used to study the statistical properties of the reactive trajectories by which…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
Connectivity is a fundamental structural feature of a network that determines the outcome of any dynamics that happens on top of it. However, an analytical approach to obtain connection probabilities between nodes associated to paths of…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot based data analysis and to widen its application potential. We will give a brief overview about important and…
Complex network theory is being widely used to study many real-life systems. One of the fields that can benefit from complex network theory approach is transportation network. In this paper, we briefly review the complex network theory…
An efficient structural identifiability analysis algorithm is developed in this study for a broad range of network structures. The proposed method adopts the Wright's path coefficient method to generate identifiability equations in forms of…