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Complex networks grow subject to structural constraints which affect their measurable properties. Assessing the effect that such constraints impose on their observables is thus a crucial aspect to be taken into account in their analysis. To…
In network theory, Pearson's correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree…
Network robustness research aims at finding a measure to quantify network robustness. Once such a measure has been established, we will be able to compare networks, to improve existing networks and to design new networks that are able to…
In this paper, we present some new results describing connections between the spectrum of a regular graph and its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.
We investigate the role of degree correlation among nodes on the stability of complex networks, by studying spectral properties of randomly weighted matrices constructed from directed Erd\"{o}s-R\'enyi and scale-free random graph models. We…
Several real-world systems can be represented as multi-layer complex networks, i.e. in terms of a superposition of various graphs, each related to a different mode of connection between nodes. Hence, the definition of proper mathematical…
The study of causal structure in complex systems has gained increasing attention, with many recent studies exploring causal networks that capture cause-effect relationships across diverse fields. Despite increasing empirical evidence…
Random networks are widely used to model complex networks and research their properties. In order to get a good approximation of complex networks encountered in various disciplines of science, the ability to tune various statistical…
In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention. While some recent studies have started to explore the relationship between the graph…
The existence or not of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking. In this work we investigate the problems of site and bond percolation on graphs with degree…
Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural…
We show that real multiplex networks are unexpectedly robust against targeted attacks on high degree nodes, and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an…
Many real-world systems are composed of many individual components that interact with one another in a complex pattern to produce diverse behaviors. Understanding how to intervene in these systems to guide behaviors is critically important…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
Complex networks often have a modular structure, where a number of tightly- connected groups of nodes (modules) have relatively few interconnections. Modularity had been shown to have an important effect on the evolution and stability of…
We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…
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…