Related papers: Explosive Percolation: Unusual Transitions of a Si…
We propose the $K$-selective percolation process as a model for the iterative removals of nodes with the specific intermediate degree in complex networks. In the model, a random node with degree $K$ is deactivated one by one until no more…
We show that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our models obtain Gaussian cluster distributions and compact clusters as…
We introduce a novel percolation model that generalizes the classical Random Connection Model (RCM) to a random simplicial complex, allowing for a more refined understanding of connectivity and emergence of large-scale structures in random…
There is still much to discover about the mechanisms and nature of discontinuous percolation transitions. Much of the past work considers graph evolution algorithms known as Achlioptas processes in which a single edge is added to the graph…
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
A first-order percolation transition, called explosive percolation, was recently discovered in evolution networks with random edge selection under a certain restriction. However, the network percolation with more realistic evolution…
We discuss several interesting random network models which exhibit (provable) explosive transitions and their applications.
For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution…
Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation…
We introduce perhaps the simplest models of graph evolution with choice that demonstrate discontinuous percolation transitions and can be analyzed via mathematical evolution equations. These models are local, in the sense that at each step…
The finite-size scaling (FSS) theory for continuous phase transitions has been useful in determining the critical behavior from the size dependent behaviors of thermodynamic quantities. When the phase transition is discontinuous, however,…
We study the percolation transition in growing networks under an Achlioptas process (AP). At each time step, a node is added in the network and, with the probability $\delta$, a link is formed between two nodes chosen by an AP. We find that…
The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is…
The evolution of the Erd\H{o}s-R\'enyi (ER) network by adding edges can be viewed as a cluster aggregation process. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection…
We consider a class of percolation models, called Achlioptas processes, discussed in [Science 323, 1453 (2009)] and [Science 333, 322 (2011)]. For these the evolution of the order parameter (the rescaled size of the largest connected…
Robustness of two coupled networks system has been studied only for dependency coupling (S. Buldyrev et. al., Nature, 2010) and only for connectivity coupling (E. A. Leicht and R. M. D'Souza, arxiv:09070894). Here we study, using a…
Critical transitions are observed in many complex systems. This includes the onset of synchronization in a network of coupled oscillators or the emergence an epidemic state within a population. "Explosive" first-order transitions have…
We propose a simple generalization of the explosive percolation process [Achlioptas et al., Science 323, 1453 (2009)], and investigate its structural and transport properties. In this model, at each step, a set of q unoccupied bonds is…
We describe the effect of power-law initial distributions of clusters on ordinary percolation and its generalizations, specifically, models of explosive percolation processes based on local optimization. These aggregation processes were…
We define a continuum percolation model that provides a collection of random ellipses on the plane and study the behavior of the covered set and the vacant set, the one obtained by removing all ellipses. Our model generalizes a construction…