Related papers: Hierarchical scale-free network is fragile against…
In this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL) which is a multi-multifractal and whose dual is a scale-free network. The characteristic properties of percolation is that it…
The impact of inhomogeneous arrangement of nodes in space on network organization cannot be neglected in most of real-world scale-free networks. Here, we wish to suggest a model for a geographical network with nodes embedded in a fractal…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…
Percolation in systems made up of randomly placed impermeable grains is often examined in the context of system spanning clusters of connected solids forming above a relatively low critical grain density $\rho_{c1}$ or networks of…
We study the mutual percolation of two interdependent lattice networks ranging from two to seven dimensions, denoted as $D$. We impose that the length of interdependent links connecting nodes in the two lattices be less than or equal to a…
The emergence of explosive collective phenomena has recently attracted much attention due to the discovery of an explosive percolation transition in complex networks. In this Letter, we demonstrate how an explosive transition shows up in…
We describe the anomalous phase transition of the emergence of the giant connected component in scale-free networks growing under mechanism of preferential linking. We obtain exact results for the size of the giant connected component and…
We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modellized by hard-core spherical particles surrounded by penetrable…
Hierarchical models of scale free networks are introduced where numbers of nodes in clusters of a given hierarchy are stochastic variables. Our models show periodic oscillations of degree distribution P(k) in the log-log scale. Periods and…
Network controllability robustness reflects how well a networked dynamical system can maintain its controllability against destructive attacks. This paper investigates the network controllability robustness from the perspective of a…
We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2-D networks, and its variants. The capacities add hierarchically down the clusters.…
The scale-free (SF) structure that commonly appears in many complex networks is one of the hot topics related to social, biological, and information sciences. The self-organized generation mechanisms are expected to be useful for efficient…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
In this work we extend the model of Bonabeau et al. in the case of scale-free networks. A sharp transition is observed from an egalitarian to an hierarchical society, with a very low population density threshold. The exact threshold value…
Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal $\Lambda $. With rigorous mathematical results we…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…
Interdependencies are ubiquitous throughout the world. Every real-world system interacts with and is dependent on other systems, and this interdependency affects their performance. In particular, interdependencies among networks make them…
Many real networks such as the World Wide Web, financial, biological, citation and social networks have a power-law degree distribution. Networks with this feature are also called scale-free. Several models for producing scale-free networks…