Related papers: Percolation in Directed Scale-Free Networks
Reciprocal arcs represent the lowest order cycle possible to find in directed graphs without self-loops. Representing also a measure of feed-back between vertices, it is interesting to understand how reciprocal arcs influence other…
We study the multifractal properties of the current distribution of the three-dimensional random resistor network at the percolation threshold. For lattices ranging in size from $8^3$ to $80^3$ we measure the second, fourth and sixth…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted…
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…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the…
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…
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…
Suspensions of hard core spherical particles of diameter $D$ with inter-core connectivity range $\delta$ can be described in terms of random geometric graphs, where nodes represent the sphere centers and edges are assigned to any two…
A general method is proposed for predicting the asymptotic percolation threshold of networks with bottlenecks, in the limit that the sub-net mesh size goes to zero. The validity of this method is tested for bond percolation on filled…
The internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to small-world and scale-free properties, clustering is the most…
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
Step strain experiments and dynamic light scattering measurements are perfomed to characterize the dynamic behavior of an o/w droplet microemulsion into which is incorporated a telechelic polymer. At sufficient droplet and polymer…
Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…
The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice $\mathbb{Z}^d$, $d\ge1$, because it fulfills several stylized facts observed in large…
In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $\tau \in (2,3)$. It is well known…
In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths…