Related papers: Spatial small-world networks: A wiring-cost perspe…

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…

In this paper, firstly, we study analytically the topological features of a family of hierarchical lattices (HLs) from the view point of complex networks. We derive some basic properties of HLs controlled by a parameter $q$. Our results…

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…

The small-world phenomenon in complex networks has been identified as being due to the presence of long-range links, i.e., links connecting nodes that would otherwise be separated by a long node-to-node distance. We find, surprisingly, that…

Power lines, roadways, pipelines and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of…

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…

Wireless network topologies change over time and maintaining routes requires frequent updates. Updates are costly in terms of consuming throughput available for data transmission, which is precious in wireless networks. In this paper, we…

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…

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…

Networks with long-range connections obeying a distance-dependent power law of sufficiently small exponent display superdiffusion, L\'evy flights and robustness properties very different from the scale-free networks. It has been proposed…

We map the conformation space of a simple lattice polymer chain to a network, where (i) the vertices of the network have a one-to-one correspondence to the conformations of the chain, and (ii) a link between two vertices indicates the…

It has been discovered recently that many social, biological and ecological systems have the so-called small-world and scale-free features, which has provoked new research interest in the studies of various complex networks. Yet, most…

Real world networks have, for a long time, been modelled by scale-free networks, which have many sparsely connected nodes and a few highly connected ones (the hubs). However, both in society and in biology, a new structure must be…

We propose a growing model which interpolates between one-dimensional regular lattice and small-world networks. The model undergoes an interesting phase transition from large to small world. We investigate the structural properties by both…

Small-world architectures may be implicated in a range of phenomena from disease propagation to networks of neurons in the cerebral cortex. While most of the recent attention on small-world networks has focussed on the effect of introducing…

Complex network formalism allows to explain the behavior of systems composed by interacting units. Several prototypical network models have been proposed thus far. The small-world model has been introduced to mimic two important features…

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…

Small-world networks are highly clustered networks with small distances among the nodes. There are many biological neural networks that present this kind of connections. There are no special weightings in the connections of most existing…

Efficiency in passage times is an important issue in designing networks, such as transportation or computer networks. The small-world networks have structures that yield high efficiency, while keeping the network highly clustered. We show…