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

Kosuke Takagi

Uwado-shinmachi 5-4, Kawagoe-shi, Saitamaken 3500817, Japan.

DOI: 10.4236/wjm.2012.24027                

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.

Keywords

Complex Networks; Scale Free; Power Law

Conflicts of Interest

The authors declare no conflicts of interest.

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