Related papers: Small-world behavior in a system of mobile element…
Connections in complex networks are inherently fluctuating over time and exhibit more dimensionality than analysis based on standard static graph measures can capture. Here, we introduce the concepts of temporal paths and distance in…
Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These…
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.…
Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these…
In this paper, we use a series of small world networks to simulate the epidemic spreading in the real world. To make our model more similar to the real world, we employ a parameter $p_{move}$ to denote its moving probability, which…
A regular lattice in which the sites can have long range connections at a distance l with a probabilty $P(l) \sim l^{-\delta}$, in addition to the short range nearest neighbour connections, shows small-world behaviour for $0 \le \delta <…
It is commonly known that there exist short paths between vertices in a network showing the small-world effect. Yet vertices, for example, the individuals living in society, usually are not able to find the shortest paths, due to the very…
In this study we have carried out computer simulations of random walks on Watts-Strogatz-type small world networks and measured the mean number of visited sites and the return probabilities. These quantities were found to obey scaling…
We consider navigation or search schemes on networks which are realistic in the sense that not all search chains can be completed. We show that the quantity $\mu = \rho/s_d$, where $s_d$ is the average dynamic shortest distance and $\rho$…
We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable…
Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such…
We study the simple random walk dynamics on an annealed version of a Small-World Network (SWN) consisting of $N$ nodes. This is done by calculating the mean number of distinct sites visited S(n) and the return probability $P_{00}(t)$ as a…
We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the…
Random walks on discrete lattices are fundamental models that form the basis for our understanding of transport and diffusion processes. For a single random walker on complex networks, many properties such as the mean first passage time and…
Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, the network behaves as a small-world. Here, we test the…
Long-distance characteristics of small-world networks have been studied by means of self-avoiding walks (SAW's). We consider networks generated by rewiring links in one- and two-dimensional regular lattices. The number of SAW's $u_n$ was…
We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities $p$ of directed random connections, a localized transient stimulus results in either self-sustained persistent activity or in a brief…
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…
Populations of mobile and communicating agents describe a vast array of technological and natural systems, ranging from sensor networks to animal groups. Here, we investigate how a group-level agreement may emerge in the continuously…
Small-world networks are highly clustered networks with small average distance among the nodes. There are many natural and technological networks that present this kind of connections. The on-off intermittency is investigated in small-world…