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We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
A fundamental problem in studying and modeling economic and financial systems is represented by privacy issues, which put severe limitations on the amount of accessible information. Here we introduce a novel, highly nontrivial method to…
We compare some methods recently used in the literature to detect the existence of a certain degree of common behavior of stock returns belonging to the same economic sector. Specifically, we discuss methods based on random matrix theory…
A market model in Stochastic Portfolio Theory is a finite system of strictly positive stochastic processes. Each process represents the capitalization of a certain stock. If at any time no stock dominates almost the entire market, which…
Multivariate Distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a Random Matrix Model for such correlated multivariate joint probability density functions that accounts for the…
We propose a multi-phase approach to explore network structures. In this method, structure analysis is not carried out on the observed network directly. Instead, certain similarity measures of the nodes are derived from the network firstly,…
The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in…
We aim to cluster financial assets in order to identify a small set of stocks to approximate the level of diversification of the whole universe of stocks. We develop a data-driven approach to clustering based on a correlation blockmodel in…
Sustainable financial markets play an important role in the functioning of human society. Still, the detection and prediction of risk in financial markets remain challenging and draw much attention from the scientific community. Here we…
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in…
We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible…
Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of…
Previous efforts in complex networks research focused mainly on the topological features of such networks, but now also encompass the dynamics. In this Letter we discuss the relationship between structure and dynamics, with an emphasis on…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
We investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks. For this we use daily return data from the NYSE and…
We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…
Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…
In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials.…
Node centrality is one of the most important and widely used concepts in the study of complex networks. Here, we extend the paradigm of node centrality in financial and economic networks to consider the changes of node "importance" produced…