Related papers: Network robustness and fragility: Percolation on r…
In this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
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.…
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently…
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. Assuming that the nodes of the wireless network are distributed as a…
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…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
It is often claimed that the entropy of a network's degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…
Many naturally occurring networks have a power-law degree distribution as well as a non-zero degree correlation. Despite this, most studies analyzing the robustness to random node-deletion and vulnerability to targeted node-deletion have…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of…
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…
The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the…
We address the problem of social network de-anonymization when relationships between people are described by scale-free graphs. In particular, we propose a rigorous, asymptotic mathematical analysis of the network de-anonymization problem…
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…
Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…