Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication...

In this paper, we propose a novel Euclidean distance preferred model yielding small-world networks in the Euclidean space, on which the epidemics dynamics is investigated. A novel local region immunization strategy is proposed to suppress the epidemic prevalence on the Euclidean small-world...

The main objective of the present paper is further to investigate global synchronization of a general model of complex delayed dynamical networks. Based on stability theory on delayed dynamical systems, some simple yet less conservative criteria for both delay-independent and delay-dependent...

In this paper, we propose a simple rule that generates scale-free small-world networks with tunable assortative coefficient. These networks are constructed by two-stage adding process for each new node. The model can reproduce scale-free degree distributions and small-world effect. The...

In this paper, by both simulations and theoretical predictions we study two and three node (or degree) correlations in random Apollonian network (RAN), which have small-world and scale-free topologies. Using the rate equation approach under the assumption of continuous degree, we first give the...

Nonextensive aspects of the degree distribution in Watts–Strogatz (WS) small-world networks, PSW(k), have been discussed in terms of a generalized Gaussian (referred to as Q-Gaussian) which is derived by the three approaches: the maximum-entropy method (MEM), stochastic differential equation...

We numerically investigate the avalanche dynamics of the Bak–Tang–Wiesenfeld sandpile model on directed small-world networks. We find that the avalanche size and duration distribution follow a power law for all rewiring probabilities p. Specially, we find that, approaching the thermodynamic...

Small-world networks are regular structures with a fraction p of regular connections per site replaced by totally random ones (“shortcuts”). This kind of structure seems to be present on networks arising in nature and technology. In this work we show that the small-world transition is a...

In this paper, the relationship between the in-degree and out-degree of World-Wide Web is studies. At each time step, a new node with out-degree kout is added, where kout obeys the power-law distribution and its mean value is m. The analytical and simulation results suggest that the exponent of...

We study the optimal distance ℓopt in random networks in the presence of disorder implemented by assigning random weights to the links. The optimal distance between two nodes is the length of the path for which the sum of weights along the path (“cost”) is a minimum. We study the case of...