World Journal of Mechanics

Volume 2, Issue 4 (August 2012)

ISSN Print: 2160-049X   ISSN Online: 2160-0503

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An Analytical Model of the Power Law Distributions in the Complex Network

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DOI: 10.4236/wjm.2012.24027    3,344 Downloads   5,550 Views  Citations
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ABSTRACT

It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One example is the scale-freeness which is described by the degree distribution in the power law shape. In this paper, within an analytical approach, we investigate the analytical conditions under which the distribution is reduced to the power law. We show that power law distributions are obtained without introducing conditions specific to each system or variable. Conversely, if we demand no special condition to a distribution, it is imposed to follow the power law. This result explains the universality and the ubiquitous presence of the power law distributions in complex networks.

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K. Takagi, "An Analytical Model of the Power Law Distributions in the Complex Network," World Journal of Mechanics, Vol. 2 No. 4, 2012, pp. 224-227. doi: 10.4236/wjm.2012.24027.

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