Related papers: Limited path percolation in complex networks
The problem of sending the maximum amount of flow $q$ between two arbitrary nodes $s$ and $t$ of complex networks along links with unit capacity is studied, which is equivalent to determining the number of link-disjoint paths between $s$…
Quantum networks (QNs) exhibit stronger connectivity than predicted by classical percolation, yet the origin of this phenomenon remains unexplored. We apply a statistical physics model -- concurrence percolation -- to uncover the origin of…
We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…
Interference management has become a key factor in regulating transmissions in wireless communication networks. To support effective interference management schemes, it can be essential to have prior knowledge about the network topology. In…
We prove three new lower bounds for graph connectivity in the $1$-bit broadcast congested clique model, BCC$(1)$. First, in the KT-$0$ version of BCC$(1)$, in which nodes are aware of neighbors only through port numbers, we show an…
This paper proposes a new model for wireless relay networks referred to as "1-2-1 network", where two nodes can communicate only if they point "beams" at each other, while if they do not point beams at each other, no signal can be exchanged…
We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a…
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. We consider the the path-loss plus fading model of wireless signal…
Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can…
The $\ell$-component connectivity (or $\ell$-connectivity for short) of a graph $G$, denoted by $\kappa_\ell(G)$, is the minimum number of vertices whose removal from $G$ results in a disconnected graph with at least $\ell$ components or a…
In reality, many real-world networks interact with and depend on other networks. We develop an analytical framework for studying interacting networks and present an exact percolation law for a network of $n$ interdependent networks (NON).…
We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after…
Dependency links in single-layer networks offer a convenient way of modeling nonlocal percolation effects in networked systems where certain pairs of nodes are only able to function together. We study the percolation properties of the weak…
Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology control algorithm. This algorithm, introduced in…
We present high statistics data on the distribution of shortest path lengths between two near-by points on the same cluster at the percolation threshold. Our data are based on a new and very efficient algorithm. For $d=2$ they clearly…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…