Power-Law Index and its Application based on the Degree of Distribution and Scale-Free Network Evolution

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Abstract: In realistic networks, many scholars have found that the connection between nodes does not only depend on the size of the node degree probability. This paper sets up a kind of changing scaling exponent scale-free network evolution model(NABA) based on the BA model. In NABA model, the preferential probability depends on sites’ degree and the growth rate of degree. Using mean field theory, we calculate the degree distribution function and give the range of scaling exponent. Furthermore we perform some simulations to testify the point of view. Simulation results verify that the distribution function is correct, and scaling exponent will vary in the range (2;+∞] with the variation of parameters. The NABA model can degenerate into BA model when = 1 and r = 0, and hence the BA model can be regarded as its special form.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #49

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Yaning Zhang, Junhai Ma, "Power-Law Index and its Application based on the Degree of Distribution and Scale-Free Network Evolution," WSEAS Transactions on Mathematics, vol. 13, pp. 505-515, 2014, DOI:
Yaning Zhang, Junhai Ma. Power-Law Index and its Application based on the Degree of Distribution and Scale-Free Network Evolution. WSEAS Transactions on Mathematics. 2014;13:505-515.
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