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
