Related papers: Disorder Induced Limited Path Percolation
One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been…
In this paper, we investigate optimal coding strategies for a class of linear deterministic relay networks. The network under study is a relay network, with one source, one destination, and two relay nodes. Additionally, there is a…
A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…
We prove non-universality results for first-passage percolation on the configuration model with i.i.d. degrees having infinite variance. We focus on the weight of the optimal path between two uniform vertices. Depending on the properties of…
In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex…
In a system of interdependent networks, an initial failure of nodes invokes a cascade of iterative failures that may lead to a total collapse of the whole system in a form of an abrupt first order transition. When the fraction of initial…
Many processes related to status, power, and influence within social networks have been modeled using forced linear diffusion models; examples include the highly successful Friedkin-Johnsen model of social influence, the status/power scores…
Recently, new results on percolation of interdependent networks have shown that the percolation transition can be first order. In this paper we show that, when considering antagonistic interactions between interacting networks, the…
Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in- and…
Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes -- in which final state can be obtained by…
Many real-world networks are coupled together to maintain their normal functions. Here we study the robustness of multiplex networks with interdependent and interconnected links under k-core percolation, where a node fails when it connects…
We consider a first neighbor interaction where agents are spread through a uni-dimensional network. Some agents are also connected to a hub, or master node, who has preferential values (or orientation). The role of master node is to…
We study the cascading failures in a system composed of two interdependent square lattice networks A and B placed on the same Cartesian plane, where each node in network A depends on a node in network B randomly chosen within a certain…
An amazingly simple model of correlated disorder is a one-dimensional chain of n potential steps with a fixed width lc and random heights. A theoretical analysis of the average transmission coefficient and Landauer resistance as functions…
We study the interplay of superconductivity and disorder by solving numerically the Bogoliubov-de-Gennes equations in a two dimensional lattice of size $80\times80$ which makes possible to investigate the weak-coupling limit. In contrast…
Interdependent networks are characterized by two kinds of interactions: The usual connectivity links within each network and the dependency links coupling nodes of different networks. Due to the latter links such networks are known to…
We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional…
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…
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,…
We study the accessibility percolation model on infinite trees. The model is defined by associating an absolute continuous random variable $X_v$ to each vertex $v$ of the tree. The main question to be considered is the existence or not of…