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We investigate how the graph topology influences the robustness to noise in undirected linear consensus networks. We measure the structural robustness by using the smallest possible value of steady state population variance of states under…
Stimulated by the growing interest in the applications of complex networks framework on time series analysis, we devise a network model in which each of $N$ nodes is associated with a random walk of length $L$. Connectivity between any two…
The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
Many real world networks are characterized by adaptive changes in their topology depending on the dynamic state of their nodes. Here we study epidemic dynamics in an adaptive network, where susceptibles are able to avoid contact with…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
Since their introduction, Boolean networks have been traditionally studied in view of their rich dynamical behavior under different update protocols and for their qualitative analogy with cell regulatory networks. More recently, tools…
Percolation on complex networks has been used to study computer viruses, epidemics, and other casual processes. Here, we present conditions for the existence of a network specific, observation dependent, phase transition in the updated…
We investigate analytically and numerically the dynamical properties of critical Boolean networks with power-law in-degree distributions. When the exponent of the in-degree distribution is larger than 3, we obtain results equivalent to…
Many real-world systems can be expressed in temporal networks with nodes playing far different roles in structure and function and edges representing the relationships between nodes. Identifying critical nodes can help us control the spread…
We investigate the avalanche temporal statistics of the Susceptible-Infected-Susceptible (SIS) model when the dynamics is critical and takes place on finite random networks. By considering numerical simulations on annealed topologies we…
The level spacing distribution is numerically calculated at the disorder-induced metal--insulator transition for dimensionality d=4 by applying the Lanczos diagonalisation. The critical level statistics are shown to deviate stronger from…
We reveal large fluctuations in the response of real multiplex networks to random damage of nodes. These results indicate that the average response to random damage, traditionally considered in mean-field approaches to percolation, is a…
We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
Using the formalism of the biased random walk in random uncorrelated networks with arbitrary degree distributions, we develop theoretical approach to the critical packet generation rate in traffic based on routing strategy with local…
Diffusion of information, behavioral patterns or innovations follows diverse pathways depending on a number of conditions, including the structure of the underlying social network, the sensitivity to peer pressure and the influence of…
Bootstrap percolation has been used effectively to model phenomena as diverse as emergence of magnetism in materials, spread of infection, diffusion of software viruses in computer networks, adoption of new technologies, and emergence of…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
Weighted networks capture the structure of complex systems where interaction strength is meaningful. This information is essential to a large number of processes, such as threshold dynamics, where link weights reflect the amount of…