相关论文: Degree and connectivity of the Internet's scale-fr…

A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free…

We study the detailed mechanism of the failure of scale-free networks under intentional attacks. Although it is generally accepted that such networks are very sensitive to targeted attacks, we show that for a particular type of structure…

Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…

To measure the IPv6 internet AS-level topology, a network topology discovery system, called Dolphin, was developed. By comparing the measurement result of Dolphin with that of CAIDA's Scamper, it was found that the IPv6 Internet at AS…

Scale-free networks are characterized by a degree distribution with power-law behavior and have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks. Degree distributions of observed…

A great deal of effort has been spent measuring topological features of the Internet. However, it was recently argued that sampling based on taking paths or traceroutes through the network from a small number of sources introduces a…

We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the…

We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)\lambda[1-(1-q)\lambda k]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $\lambda$. We study the…

Scale-free networks with moderate edge dependence experience a phase transition between ultrasmall and small world behaviour when the power law exponent passes the critical value of three. Moreover, there are laws of large numbers for the…

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…

We investigate the higher-order connectivity of scale-free networks using algebraic topology. We model scale-free networks as preferential attachment graphs, and we study the algebraic-topological properties of their clique complexes. We…

We study scale free simple graphs with an exponent of the degree distribution $\gamma$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units…

Using a steady state process of node duplication and deletion we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. This occurs even though there is no growth involved and inherent preferential…

Recently there have been a tremendous interest in models of networks with a power-law distribution of degree -- so called "scale-free networks." It has been observed that such networks, normally, have extremely short path-lengths, scaling…

We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an…

We calculate the mean neighboring degree function $\bar k_{\rm{nn}}(k)$ and the mean clustering function $C(k)$ of vertices with degree $k$ as a function of $k$ in finite scale-free random networks through the static model. While both are…

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

We study the mean length $\ell(k)$ of the shortest paths between a vertex of degree $k$ and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law…

The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…