We propose a general geometric growth model for pseudofractal scale-free web (PSW), which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks: degree distribution, second moment of degree distribution, degree correlations, distribution of...

We propose a simple algorithm which produces a new category of networks, high-dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension...

Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are stochastic, that is they create networks in which the nodes...

The world-wide web forms a large directed graph, whose vertices are documents and edges are links pointing from one document to another. Here we demonstrate that despite its apparent random character, the topology of this graph has a number of universal scale-free characteristics. We introduce a...

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study...

We study a self-organized scale-free network model generated using the Merging-and-Creation dynamics with preferential attachment. We show analytically that the introduction of preferential attachment has minimal impact on the steady-state degree distribution. However, we find also that the...

We present a model of network formation where entering nodes find other nodes to link to both completely at random and through search of the neighborhoods of these randomly met nodes. We show that this model exhibits the full spectrum of features that have been found to characterize large...

When we study the architecture of networks of spatially extended systems the nodes in the network are subject to local correlation structures. In this case, we show that for scale-free networks the traditional way to estimate the clustering coefficient may not be meaningful. Here we explain why...

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...

We present a simple mechanism for generating undirected scale-free networks using random walkers, where the network growth is determined by choosing parent vertices by sequential random walks. We show that this mechanism produces scale-free networks with degree exponent γ=3 and clustering...