Related papers: Percolation of partially interdependent networks u…
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…
The internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to small-world and scale-free properties, clustering is the most…
Targeted immunization or attacks of large-scale networks has attracted significant attention by the scientific community. However, in real-world scenarios, knowledge and observations of the network may be limited thereby precluding a full…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
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.…
We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, the strategies for enhancing robustness and immunization of a…
Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the…
Interconnected networks have been shown to be much more vulnerable to random and targeted failures than isolated ones, raising several interesting questions regarding the identification and mitigation of their risk. The paradigm to address…
In this paper, robustness of planar trivalent random graphs to targeted attacks of highest connected nodes is investigated using numerical simulations. It is shown that these graphs are relatively robust. The nonrandom node removal process…
Extraction of interaction networks from multi-variate time-series is one of the topics of broad interest in complex systems. Although this method has a wide range of applications, most of the previous analyses have focused on the pairwise…
We study both numerically and analytically what happens to a random graph of average connectivity "alpha" when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated…
The intrinsically secure communications graph (iS-graph) is a random graph which captures the connections that can be securely established over a large-scale network, in the presence of eavesdroppers. It is based on principles of…
Quantum networks are essential to quantum information distributed applications, and communicating over them is a key challenge. Complex networks have rich and intriguing properties, which are as yet unexplored in the quantum setting. Here,…
Spread of information in crowd is analysed in terms of directed percolation in two-dimensional spatial network. We investigate the case when the information transmitted can be incomplete or damaged. The results indicate that for small or…
We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs as well as random graphs, and investigate their relations to classical percolation theory, more particularly the impact of Bernoulli bond…
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…
We investigate the steady state of a two-dimensional random resistor network subjected to two competing biased percolations as a function of the bias strength. The properties of the linear and nonlinear regimes are studied by means of Monte…
The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, the study on the connections between…
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…
We analyze critical phenomena on networks generated as the union of hidden variables models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small-worlds similar to those a` la Watts and…