Related papers: Percolation Theory on Interdependent Networks Base…
Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network…
In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…
In the last two decades, network science has blossomed and influenced various fields, such as statistical physics, computer science, biology and sociology, from the perspective of the heterogeneous interaction patterns of components…
The recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies…
We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an…
Edge-based percolation methods can be used to analyze disease transmission on complex social networks. This allows us to include complex social heterogeneity in our models while maintaining tractability. Here we review the seminal works on…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
It was recently found that cascading failures can cause the abrupt breakdown of a system of interdependent networks. Using the percolation method developed for single clustered networks by Newman [Phys. Rev. Lett. {\bf 103}, 058701 (2009)],…
Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally tree-like ansatz. Such an approximation, however, holds only to a limited extent, as real graphs are often…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{et al}. Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif…
Connectivity and reachability on temporal networks, which can describe the spreading of a disease, decimation of information or the accessibility of a public transport system over time, have been among the main contemporary areas of study…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
Real data show that interdependent networks usually involve inter-similarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent (Parshani et al \cite{PAR10B}). For…
In this paper we study the interplay between epidemic spreading and risk perception on multiplex networks. The basic idea is that the effective infection probability is affected by the perception of the risk of being infected, which we…
A central concern of network operators is to estimate the probability of an incident that affects a significant part and thus may yield to a breakdown. We answer this question by modeling how a failure of either a node or an edge will…
Interdependencies are ubiquitous throughout the world. Every real-world system interacts with and is dependent on other systems, and this interdependency affects their performance. In particular, interdependencies among networks make them…
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…