While the emergence of a power-law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the between ness centrality displays a power-law distribution with an exponent eta, which is robust, and use it to classify the scale-free networks. We have observed two universality classes with eta approximately equal 2.2(1) and 2.0, respectively. R...

The increased availability of data on real networks has favoured an explosion of activity in the elaboration of models able to reproduce both qualitatively and quantitatively the measured properties. What has been less explored is the reliability of the data, and whether the measurement technique biases them. Here we show that tree-like explorations (similar in principle to traceroute) can inde...

where qk is the probability that a randomly chosen node has degree k, and cγ and γ are positive constants. As this formula makes sense only for k > 0, we will tacitly assume that the graph contains no isolated nodes, that is, q0 = 0. Graphs with a power-law distribution of degrees are often called scale-free networks. This phrase needs to be handled with care. Since qk > 0 for all k > 1, Equati...

We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) proportional, variant k(-lambda), i.e., the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small-world networks, which is known to be d approximately ln(N, we show, using analytical arguments, that scale-fr...

In this paper, we present a new simulation tool for scale-free networks composed of a high number of nodes. The tool, based on discrete-event simulation, enables the definition of scale-free networks composed of heterogeneous nodes and complex application-level protocols. To satisfy the performance and scalability requirements, the simulator supports both sequential (i.e. monolithic) and parall...

In this paper, we proposed an ungrowing scale-free network model, indicating the growth may not be a necessary condition of the self-organization of a network in a scale-free structure. The analysis shows that the degree distributions of the present model can varying from the Poisson form to the power-law form with the decrease of a free parameter α. This model provides a possible mechanism for...

We have studied nucleation dynamics of the Ising model in scale-free networks whose degree distribution follows a power law with the exponent γ by using the forward flux sampling method and focusing on how the network topology would influence the nucleation rate and pathway. For homogeneous nucleation, the new phase clusters grow from those nodes with smaller degree, while the cluster sizes fol...

Growth and preferential attachments have been coined as the two fundamental mechanisms responsible for the scale-free feature in complex networks, as characterized by an algebraic degree distribution. There are situations, particularly in biological networks, where growth is absent or not important, yet some of these networks still exhibit the scale-free feature with a small degree exponent. He...