Related papers: Using explosive percolation in analysis of real-wo…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…
A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to…
We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erd\H{o}s--R\'{e}nyi random graph that incorporates the community structure observed in many real systems. In the SBM, nodes are…
Models of percolation processes on networks currently assume locally tree-like structures at low densities, and are derived exactly only in the thermodynamic limit. Finite size effects and the presence of short loops in real systems however…
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…
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…
We study an explosive percolation model in which a link is randomly added and neighboring nodes sequentially rewire their links to suppress the growth of large clusters. In this manner, the rewiring nodes spread outward starting from the…
The existence of explosive phase transitions in random (Erd\H os R\'enyi-type) networks has been recently documented by Achlioptas et al.\ [Science {\bf 323}, 1453 (2009)] via simulations. In this Letter we describe the underlying mechanism…
Networks composed from both connectivity and dependency links were found to be more vulnerable compared to classical networks with only connectivity links. Their percolation transition is usually of a first order compared to the second…
Social reinforcement and modular structure are two salient features observed in the spreading of behavior through social contacts. In order to investigate the interplay between these two features, we study the generalized epidemic process…
The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks…
In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…
Percolation theory has been widely used to study phase transitions in complex networked systems. It has also successfully explained several macroscopic phenomena across different fields. Yet, the existent theoretical framework for…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
In this Letter, we show that the explosive percolation is a novel continuous phase transition. The order-parameter-distribution histogram at the percolation threshold is studied in Erd\H{o}s-R\'{e}nyi networks, scale-free networks, and…
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…
Many real-world complex systems such as social, biological, information as well as technological systems results of a decentralized and unplanned evolution which leads to a common structuration. Irrespective of their origin, these so-called…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…
Quantum communication demands efficient distribution of quantum entanglement across a network of connected partners. The search for efficient strategies for the entanglement distribution may be based on percolation theory, which describes…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. Clustering, community structure and assortative mixing by degree are perhaps among most prominent…