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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…
This paper summarizes the state of knowledge and ongoing research on methods and techniques for resilience evaluation, taking into account the resilience-scaling challenges and properties related to the ubiquitous computerized systems. We…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
We consider a multi-layer network with two layers, $\mathcal{L}_{1}$, $\mathcal{L}_{2}$. Their intra-layer topology shows a scale-free degree distribution and a core-periphery structure. A nested structure describes the inter-layer…
Understanding and characterizing the vulnerability of urban infrastructures, which refers to the engineering facilities essential for the regular running of cities and that exist naturally in the form of networks, is of great value to us.…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
Detecting and characterizing community structure plays a crucial role in the study of networked systems. However, there is still a lack of understanding of how community structure affects the systems' resilience and stability. Here, we…
This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
In the analysis of the robustness of multiplex networks, it is commonly assumed that a node is functioning only if its interdependent nodes are simultaneously functioning. According to this model, a multiplex network becomes more and more…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…
Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in- and…
Scale-free percolation is a stochastic model for complex networks. In this spatial random graph model, vertices $x,y\in\mathbb{Z}^d$ are linked by an edge with probability depending on i.i.d.\ vertex weights and the Euclidean distance…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
We propose a method of generating different scale-free networks, which has several input parameters in order to adjust the structure, so that they can serve as a basis for computer simulation of real-world phenomena. The topological…
This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and…
It has been found that the networks with scale-free distribution are very resilient to random failures. The purpose of this work is to determine the network design guideline which maximize the network robustness to random failures with the…
This work presents a new method to quantify connectivity in transportation networks. Inspired by the field of topological data analysis, we propose a novel approach to explore the robustness of road network connectivity in the presence of…