Related papers: Small Worlds: Strong Clustering in Wireless Networ…

We introduce a model for a preferentially attached network which has grown from a small world network. Here, the average path length and the clustering coefficient are estimated, and the topological properties of modeled networks are…

We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…

Small world networks interpolate between fully regular and fully random topologies and simultaneously exhibit large local clustering as well as short average path length. Small world topology has therefore been suggested to support network…

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…

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…

Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…

Navigability of networks, that is the ability to find any given destination vertex starting from any other vertex, is crucial to their usefulness. In 2000 Kleinberg showed that optimal navigability could be achieved in small-world networks…

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…

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…

We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the…

Dating back to two famous experiments by the social-psychologist, Stanley Milgram, in the 1960s, the small-world phenomenon is the idea that all people are connected through a short chain of acquaintances that can be used to route messages.…

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…

Both small world models of random networks with occasional long range connections and gossip processes with occasional long range transmission of information have similar characteristic behaviour. The long range elements appreciably reduce…

The small-world phenomenon is found in many self-organising systems. Systems configured in small-world networks spread information more easily than in random or regular lattice-type networks. Whilst it is a known fact that small-world…

We characterize the distributions of short cycles in a large metabolic network previously shown to have small world characteristics and a power law degree distribution. Compared with three classes of random networks, including Erdoes-Renyi…

Strong inter-dependence in complex systems can manifest as partially bipartite networks characterized by interactions occurring primarily between distinct groups of nodes (identified as modules). In this paper, we show that the anti-modular…

In this paper we consider spatial networks that realize a balance between an infrastructure cost (the cost of wire needed to connect the network in space) and communication efficiency, measured by average shortest pathlength. A global…

Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…

Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…

Understanding the topological characteristics of complex networks and how they affect navigability is one of the most important goals in science today, as it plays a central role in various economic, biological, ecological and social…