Related papers: Avalanche-size distribution of Cayley tree
A probabilistic framework is introduced that represents stylized banking networks and aims to predict the size of contagion events. In contrast to previous work on random financial networks, which assumes independent connections between…
We prove rigorously several results about the site-percolation on random recursive trees, observed in the previous work by Kalay and Ben-Naim [J. Phys. A48(2015), no.4, 0405001, 15 pp.]. For a random recursive tree of size $n$, let every…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
We reveal large fluctuations in the response of real multiplex networks to random damage of nodes. These results indicate that the average response to random damage, traditionally considered in mean-field approaches to percolation, is a…
Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics.…
In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…
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…
In many cases of attacks or failures, memory effects play a significant role. Therefore, we present a model that not only considers the dependencies between nodes but also incorporates the memory effects of attacks. Our research…
If we add links to a network at random, a critical threshold can be crossed where a giant connected component forms. Conversely, if links or nodes are removed at random, the giant component shrinks and eventually breaks. In this paper, we…
It is commonly believed that scale-free networks are robust to massive numbers of random node deletions. For example, Cohen et al. study scale-free networks including some which approximate the measured degree distribution of the Internet.…
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.…
We present a new inference method based on approximate Bayesian computation for estimating parameters governing an entire network based on link-traced samples of that network. To do this, we first take summary statistics from an observed…
A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k)=ck^-a. We study the stability of such networks with respect to crashes, such…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
Scale-free networks with small power law exponent are known to be robust, meaning that their qualitative topological structure cannot be altered by random removal of even a large proportion of nodes. By contrast, it has been argued in the…
Susceptibility of scale free Power Law (PL) networks to attacks has been traditionally studied in the context of what may be termed as {\em instantaneous attacks}, where a randomly selected set of nodes and edges are deleted while the…
Multilayer networks have been found to be prone to abrupt cascading failures under random and targeted attacks, but most of the targeting algorithms proposed so far have been mainly tested on uncorrelated systems. Here we show that the size…
We study the statistical properties of the SIR epidemics in heterogeneous networks, when an epidemic is defined as only those SIR propagations that reach or exceed a minimum size s_c. Using percolation theory to calculate the average…
We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…
We introduce a toy model displaying the avalanche dynamics of failure in scale-free networks. In the model, the network growth is based on the Barab\'asi and Albert model and each node is assigned a capacity or tolerance, which is constant…