Related papers: Neighbor-induced damage percolation
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…
The model of random interlacements on Z^d, d bigger or equal to 3, was recently introduced in arXiv:0704.2560. A non-negative parameter u parametrizes the density of random interlacements on Z^d. In the present note we investigate the…
We describe the component sizes in critical independent p-bond percolation on a random d-regular graph on n vertices, where d \geq 3 is fixed and n grows. We prove mean-field behavior around the critical probability p_c=1/(d-1). In…
Jigsaw percolation is a model for the process of solving puzzles within a social network, which was recently proposed by Brummitt, Chatterjee, Dey and Sivakoff. In the model there are two graphs on a single vertex set (the `people' graph…
On a large finite connected graph let edges $e$ become "open" at independent random Exponential times of arbitrary rates $w_e$. Under minimal assumptions, the time at which a giant component starts to emerge is weakly concentrated around…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
We introduce a class of damage models on regular lattices with isotropic interactions, as e.g. quasistatic fiber bundles. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated…
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…
The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…
Most networks of interest do not live in isolation. Instead they form components of larger systems in which multiple networks with distinct topologies coexist and where elements distributed amongst different networks may interact directly.…
Percolation on a five-dimensional simple hypercubic (sc(5)) lattice with extended neighborhoods is investigated by means of extensive Monte Carlo simulations, using an effective single-cluster growth algorithm. The critical exponents,…
In this paper we focus on $r$-neighbor bootstrap percolation, which is a process on a graph where initially a set $A_0$ of vertices gets infected. Now subsequently, an uninfected vertex becomes infected if it is adjacent to at least $r$…
The models of $k$-core percolation and interdependent networks (IN) have been extensively studied in their respective fields. A recent study has revealed that they share several common critical exponents. However, several newly discovered…
In the last decades, many authors have used the susceptible-infected-recovered model to study the impact of the disease spreading on the evolution of the infected individuals. However, few authors focused on the temporal unfolding of the…
Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to…
Consider the long-range models on $\mathbb{Z}^d$ of random walk, self-avoiding walk, percolation and the Ising model, whose translation-invariant 1-step distribution/coupling coefficient decays as $|x|^{-d-\alpha}$ for some $\alpha>0$. In…
Edges, binding together nodes within networks, have the potential to induce dramatic transitions when specific collective failure behaviors emerge. These changes, initially unfolding covertly and then erupting abruptly, pose substantial,…
We address the problem of disentangled representation learning with independent latent factors in graph convolutional networks (GCNs). The current methods usually learn node representation by describing its neighborhood as a perceptual…
Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks, in which the…
The study of interdependent networks, and in particular the robustness on networks, has attracted considerable attention. Recent studies mainly assume that the dependence is fully interdependent. However, targeted attack for partially…