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Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…

This paper introduces a novel framework that combines traditional centrality measures with eigenvalue spectra and diffusion processes for a more comprehensive analysis of complex networks. While centrality measures such as degree,…

We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…

We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate…

We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…

A minimal model for self-organized critical percolation on directed graphs with activating and de-activating links is studied. Unlike classical self-organized criticality, the variables that determine criticality are separated from the…

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…

We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…

Cascading failures and epidemic dynamics, as two successful application realms of network science, are usually investigated separately. How do they affect each other is still one open, interesting problem. In this letter, we couple both…

The ability to understand and eventually predict the emergence of information and activation cascades in social networks is core to complex socio-technical systems research. However, the complexity of social interactions makes this a…

We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…

Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of…

We investigate percolation on growing networks where the evolution of connected components resembles a non-equilibrium version of the multiplicative coalescent. The supercritical $\pi> \pi_c$ regime for a host of such models was conjectured…

Because of the non-uniformity of the electric power CPS network and the dynamic nature of the risk propagation process, it is difficult to quantify the critical point of a cyber risk explosion. From the perspective of the dependency…

We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network…

Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…

Drawing inspiration from real world interacting systems we study a system consisting of two networks that exhibit antagonistic and dependent interactions. By antagonistic and dependent interactions, we mean, that a proportion of functional…

Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions,…

We study the problem of wireless network resilience to node failures from a percolation-based perspective. In practical wireless networks, it is often the case that the failure probability of a node depends on its degree (number of…

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…