Related papers: Relaxation Properties of Small-World Networks
The small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)] has attracted much interests in studying the interesting properties of the networks without time-delay. However, a signal or influence travelling on…
Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph…
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…
Small-world networks by Watts and Strogatz are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. These characteristics result in networks with unique…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
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…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…
Many geophysical processes can be modelled by using interconnected networks. The small-world network model has recently attracted much attention in physics and applied sciences. In this paper, we try to use and modify the small-world theory…
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…
The Small-World phenomenon, popularly known as six degrees of separation, has been mathematically formalized by Watts and Strogatz in a study of the topological properties of a network. Small-worlds networks are defined in terms of two…
Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…
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…
We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…
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…
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…
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 computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…
Real-world dynamics running on networks can be characterized in terms of their respective diversity, or heterogeneity of state values. Spatial networks can be understood as networks exhibiting limited small world characteristics. In the…
We investigate small-world networks from the point of view of their origin. While the characteristics of small-world networks are now fairly well understood, there is as yet no work on what drives the emergence of such a network…