Related papers: Jigsaw percolation on random hypergraphs
Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…
In r-neighbour bootstrap percolation on a graph G, a set of initially infected vertices A \subset V(G) is chosen independently at random, with density p, and new vertices are subsequently infected if they have at least r infected…
In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models of random graphs when considered at criticality. Specifically, we apply our…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
By bootstrap percolation we mean the following deterministic process on a graph $G$. Given a set $A$ of vertices "infected" at time 0, new vertices are subsequently infected, at each time step, if they have at least $r\in\mathbb{N}$…
Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph…
Consider a bipartite random geometric graph on the union of two independent homogeneous Poisson point processes in $d$-space, with distance parameter $r$ and intensities $\lambda,\mu$. We show for $d \geq 2$ that if $\lambda$ is…
The `random intersection graph with communities' models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that nodes can merge into clusters only if they…
In this paper we propose a method of proving impossibility results based on applying strong data-processing inequalities to estimate mutual information between sets of variables forming certain Markov random fields. The end result is that…
As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two $k$-cliques means that they share at least $l<k$ vertices. In this paper, we develop a theoretical…
We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a…
On a geometric model for complex networks (introduced by Krioukov et al.) we investigate the bootstrap percolation process. This model consists of random geometric graphs on the hyperbolic plane having $N$ vertices, a dependent version of…
Motivated by the success of a k-clique percolation method for the identification of overlapping communities in large real networks, here we study the k-clique percolation problem in the Erdos-Renyi graph. When the probability p of two nodes…
We study random subcube intersection graphs, that is, graphs obtained by selecting a random collection of subcubes of a fixed hypercube $Q_d$ to serve as the vertices of the graph, and setting an edge between a pair of subcubes if their…
In complex network research clique percolation, introduced by Palla et al., is a deterministic community detection method, which allows for overlapping communities and is purely based on local topological properties of a network. Here we…
Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a…
Distributed consensus computation over random graph processes is considered. The random graph process is defined as a sequence of random variables which take values from the set of all possible digraphs over the node set. At each time step,…