Related papers: Discontinuous percolation via suppression of neigh…
When a link is occupied to restrict the growth of large clusters using the size information of a finite number of finite clusters, so-called local information, an abrupt but continuous transition is exhibited. We report here that a hybrid…
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…
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…
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,…
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…
Bootstrap percolation is a prominent framework for studying the spreading of activity on a graph. We begin with an initial set of active vertices. The process then proceeds in rounds, and further vertices become active as soon as they have…
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…
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 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…
Understanding what types of phenomena lead to discontinuous phase transitions in the connectivity of random networks is an outstanding challenge. Here we show that a simple stochastic model of graph evolution leads to a discontinuous…
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…
We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is…
We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases, goes through a minimum and…
We introduce a bond percolation procedure on a $D$-dimensional lattice where two neighbouring sites are connected by $N$ channels, each operated by valves at both ends. Out of a total of $N$, randomly chosen $n$ valves are open at every…
When a group of people unknown to each other meet and familiarize among themselves, over time they form a community on a macroscopic scale. This phenomenon can be understood in the context of percolation transition (PT) of networks, which…
Multilayer infrastructure is often interdependent, with nodes in one layer depending on nearby nodes in another layer to function. The links in each layer are often of limited length, due to the construction cost of longer links. Here, we…
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, $p\nearrow p_{c}$. To this end, we…
A random growth lattice filling model of percolation with touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty sites and…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
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…