Related papers: Percolation Transitions in Growing Networks Under …
Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem.…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
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…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
We introduce an exponential random graph model for networks with a fixed degree distribution and with a tunable degree-degree correlation. We then investigate the nature of a percolation transition in the correlated network with the Poisson…
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…
Many interdependent, real-world infrastructures involve interconnections between different communities or cities. Here we study if and how the effects of such interconnections can be described as an external field for interdependent…
The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size $N$ as $N^\psi$ and the mean number of clusters with size $s$ per node follows a power function $n_s…
Explosive percolation in the Achlioptas process has recently attracted much research attention. From extensive simulations in an event-based ensemble, we find that, in dimensions from $2$ to $6$ and on random graphs, the Achlioptas…
Clusters generated by the product-rule growth model of Achlioptas, D'Souza, and Spencer on a two-dimensional square lattice are shown to obey qualitatively different scaling behavior than standard (random growth) percolation. The threshold…
We study the percolation phase transition on preferential attachment models, in which vertices enter with $m$ edges and attach proportionally to their degree plus $\delta$. We identify the critical percolation threshold as…
We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field…
We investigate a model protein interaction network whose links represent interactions between individual proteins. This network evolves by the functional duplication of proteins, supplemented by random link addition to account for…
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…
Random graph models with limited choice have been studied extensively with the goal of understanding the mechanism of the emergence of the giant component. One of the standard models are the Achlioptas random graph processes on a fixed set…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…