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A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P ( k ) of nodes in the network having k connections to other nodes goes for large values of k as
This distribution is a common alternative to the asymptotic power-law distribution because it naturally captures finite-size effects. The Tweedie distributions are a family of statistical models characterized by closure under additive and reproductive convolution as well as under scale transformation. Consequently, these models all express a ...
A scale-free network is a type of networks that is of particular interest of network science.It is characterized by its degree distribution following a power law. While the most widely known generative models for scale-free networks are stochastic, such as the Barabási–Albert model or the Fitness model can reproduce many properties of real-life networks by assuming preferential attachment ...
A network is called scale-free [6] [14] if its degree distribution, i.e., the probability that a node selected uniformly at random has a certain number of links (degree), follows a mathematical function called a power law. The power law implies that the degree distribution of these networks has no characteristic scale.
The degree distribution of the BA Model, which follows a power law. In loglog scale the power law function is a straight line. [26] The degree distribution resulting from the BA model is scale free, in particular, for large degree it is a power law of the form: ()
The distribution of the vertex degrees of a BA graph with 200000 nodes and 2 new edges per step. Plotted in log-log scale. It follows a power law with exponent -2.78. The degree distribution resulting from the BA model is scale free, in particular, it is a power law of the form ()
In a scale-free network the degree distribution follows a power law function. In some empirical examples this power-law fits the degree distribution well only in the high degree region; in some small degree nodes the empirical degree-distribution deviates from it. See for example the network of scientific citations. [1]
It can be shown, that such a network produces a power law degree distribution, with an exponent = where is the ratio of number of the randomly added edges to the number of the copied edges. [3] So with a ratio between zero and 0.5 a power law distribution with an exponent of 2 < γ < 3 {\displaystyle 2<\gamma <3} can be achieved.