Scale free distribution in an analytical approach

In order to explain the scale free feature of complex networks, we introduce an analytical approach for investigating the degree distribution. We represent the degree distribution by the probability density function, where the correspondence between them is given approximately by the transformation from discrete number, degree, to a continuous variable. We find that arbitrary representations of the degree distribution as the probability density function are reduced to a specific form which obeys scale free. Our result provides one explanation for the ubiquity of scale free networks.