Related papers: Scaling and percolation in the small-world network…
Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a pre-critical to the…
We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the coevolution of topology and weight. In the model, we have the degree distribution exponent $\gamma$ restricted to a range between 2…
We study some simple models of disease transmission on small-world networks, in which either the probability of infection by a disease or the probability of its transmission is varied, or both. The resulting models display epidemic behavior…
Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…
Small-world networks, known for high local clustering and short path lengths, are a fundamental structure in many real-world systems, including social, biological, and technological networks. We apply the theory of (marked) local…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems.…
We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…
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…
We study percolation on small-world networks, which has been proposed as a simple model of the propagation of disease. The occupation probabilities of sites and bonds correspond to the susceptibility of individuals to the disease and the…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…
Navigation process is studied on a variant of the Watts-Strogatz small world network model embedded on a square lattice. With probability $p$, each vertex sends out a long range link, and the probability of the other end of this link…
In this paper we introduce a new model of data packet transport, based on a stochastic approach with the aim of characterizing the load distribution on complex networks. Moreover we analyze the load standard deviation as an index of…
In the last two decades, network science has blossomed and influenced various fields, such as statistical physics, computer science, biology and sociology, from the perspective of the heterogeneous interaction patterns of components…
Small-world networks---complex networks characterized by a combination of high clustering and short path lengths---are widely studied using the paradigmatic model of Watts and Strogatz (WS). Although the WS model is already quite minimal…
Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…
We study the small-world networks recently introduced by Watts and Strogatz [Nature {\bf 393}, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…
It is known that the critical probability for the percolation transition is not a sharp threshold, actually it is a region of non-zero width $\Delta p_c$ for systems of finite size. Here we present evidence that for complex networks $\Delta…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…